3.73.2 $\int \frac{3125-9395x+1867x^2+8632x^3-6351x^4+566x^5+832x^6-304x^7+32x^8+(6250-3125x-5625x^2+4750x^3-200x^4-864x^5+304x^6-32x^7)\log (2+x)+(6250x-9385x^2+3749x^3+1002x^4-1200x^5+336x^6-32x^7+(-6250+9375x-3750x^2-1000x^3+1200x^4-336x^5+32x^6)\log (2+x))\log (\frac{625x-1001x^2+600x^3-160x^4+16x^5+(-625+1000x-600x^2+160x^3-16x^4)\log (2+x)}{625-1000x+600x^2-160x^3+16x^4})}{-6250x^2+9385x^3-3749x^4-1002x^5+1200x^6-336x^7+32x^8+(6250x-9375x^2+3750x^3+1000x^4-1200x^5+336x^6-32x^7)\log (2+x)+(6250x-9385x^2+3749x^3+1002x^4-1200x^5+336x^6-32x^7+(-6250+9375x-3750x^2-1000x^3+1200x^4-336x^5+32x^6)\log (2+x))\log (\frac{625x-1001x^2+600x^3-160x^4+16x^5+(-625+1000x-600x^2+160x^3-16x^4)\log (2+x)}{625-1000x+600x^2-160x^3+16x^4})}dx$

Optimal. Leaf size=29 $$1+x+\log (-x+\log (x-\frac{x^2}{(5-2x{)}^4}-\log (2+x)))$$

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Rubi [F]  time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.000, Rules used = {} $$\begin{array}{c}\text{\$Aborted}\end{array}$$

Verification is not applicable to the result.

[In]

Int[(3125 - 9395*x + 1867*x^2 + 8632*x^3 - 6351*x^4 + 566*x^5 + 832*x^6 - 304*x^7 + 32*x^8 + (6250 - 3125*x -
5625*x^2 + 4750*x^3 - 200*x^4 - 864*x^5 + 304*x^6 - 32*x^7)*Log[2 + x] + (6250*x - 9385*x^2 + 3749*x^3 + 1002*
x^4 - 1200*x^5 + 336*x^6 - 32*x^7 + (-6250 + 9375*x - 3750*x^2 - 1000*x^3 + 1200*x^4 - 336*x^5 + 32*x^6)*Log[2
+ x])*Log[(625*x - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5 + (-625 + 1000*x - 600*x^2 + 160*x^3 - 16*x^4)*Log[2
+ x])/(625 - 1000*x + 600*x^2 - 160*x^3 + 16*x^4)])/(-6250*x^2 + 9385*x^3 - 3749*x^4 - 1002*x^5 + 1200*x^6 -
336*x^7 + 32*x^8 + (6250*x - 9375*x^2 + 3750*x^3 + 1000*x^4 - 1200*x^5 + 336*x^6 - 32*x^7)*Log[2 + x] + (6250*
x - 9385*x^2 + 3749*x^3 + 1002*x^4 - 1200*x^5 + 336*x^6 - 32*x^7 + (-6250 + 9375*x - 3750*x^2 - 1000*x^3 + 120
0*x^4 - 336*x^5 + 32*x^6)*Log[2 + x])*Log[(625*x - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5 + (-625 + 1000*x - 60
0*x^2 + 160*x^3 - 16*x^4)*Log[2 + x])/(625 - 1000*x + 600*x^2 - 160*x^3 + 16*x^4)]),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.32, size = 44, normalized size = 1.52 $$\begin{array}{c}x+\log (x-\log (\frac{x(625-1001x+600x^2-160x^3+16x^4)}{(5-2x{)}^4}-\log (2+x)))\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(3125 - 9395*x + 1867*x^2 + 8632*x^3 - 6351*x^4 + 566*x^5 + 832*x^6 - 304*x^7 + 32*x^8 + (6250 - 312
5*x - 5625*x^2 + 4750*x^3 - 200*x^4 - 864*x^5 + 304*x^6 - 32*x^7)*Log[2 + x] + (6250*x - 9385*x^2 + 3749*x^3 +
1002*x^4 - 1200*x^5 + 336*x^6 - 32*x^7 + (-6250 + 9375*x - 3750*x^2 - 1000*x^3 + 1200*x^4 - 336*x^5 + 32*x^6)
*Log[2 + x])*Log[(625*x - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5 + (-625 + 1000*x - 600*x^2 + 160*x^3 - 16*x^4)
*Log[2 + x])/(625 - 1000*x + 600*x^2 - 160*x^3 + 16*x^4)])/(-6250*x^2 + 9385*x^3 - 3749*x^4 - 1002*x^5 + 1200*
x^6 - 336*x^7 + 32*x^8 + (6250*x - 9375*x^2 + 3750*x^3 + 1000*x^4 - 1200*x^5 + 336*x^6 - 32*x^7)*Log[2 + x] +
(6250*x - 9385*x^2 + 3749*x^3 + 1002*x^4 - 1200*x^5 + 336*x^6 - 32*x^7 + (-6250 + 9375*x - 3750*x^2 - 1000*x^3
+ 1200*x^4 - 336*x^5 + 32*x^6)*Log[2 + x])*Log[(625*x - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5 + (-625 + 1000*
x - 600*x^2 + 160*x^3 - 16*x^4)*Log[2 + x])/(625 - 1000*x + 600*x^2 - 160*x^3 + 16*x^4)]),x]

[Out]

x + Log[x - Log[(x*(625 - 1001*x + 600*x^2 - 160*x^3 + 16*x^4))/(5 - 2*x)^4 - Log[2 + x]]]

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fricas [B]  time = 0.57, size = 81, normalized size = 2.79 $$\begin{array}{c}x+\log (-x+\log \left(\frac{16x^5-160x^4+600x^3-1001x^2-(16x^4-160x^3+600x^2-1000x+625)\log (x+2)+625x}{16x^4-160x^3+600x^2-1000x+625}\right))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+
3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+6
25*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+304*x^6-864*x^5-200*x^4+4750*x^3-5625*x^2-3125*x+6250)*log
(2+x)+32*x^8-304*x^7+832*x^6+566*x^5-6351*x^4+8632*x^3+1867*x^2-9395*x+3125)/(((32*x^6-336*x^5+1200*x^4-1000*x
^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160
*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+
(-32*x^7+336*x^6-1200*x^5+1000*x^4+3750*x^3-9375*x^2+6250*x)*log(2+x)+32*x^8-336*x^7+1200*x^6-1002*x^5-3749*x^
4+9385*x^3-6250*x^2),x, algorithm="fricas")

[Out]

x + log(-x + log((16*x^5 - 160*x^4 + 600*x^3 - 1001*x^2 - (16*x^4 - 160*x^3 + 600*x^2 - 1000*x + 625)*log(x +
2) + 625*x)/(16*x^4 - 160*x^3 + 600*x^2 - 1000*x + 625)))

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giac [B]  time = 3.37, size = 93, normalized size = 3.21 $$\begin{array}{c}x+\log (x-\log (16x^5-16x^4\log (x+2)-160x^4+160x^3\log (x+2)+600x^3-600x^2\log (x+2)-1001x^2+1000x\log (x+2)+625x-625\log (x+2))+\log (16x^4-160x^3+600x^2-1000x+625))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+
3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+6
25*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+304*x^6-864*x^5-200*x^4+4750*x^3-5625*x^2-3125*x+6250)*log
(2+x)+32*x^8-304*x^7+832*x^6+566*x^5-6351*x^4+8632*x^3+1867*x^2-9395*x+3125)/(((32*x^6-336*x^5+1200*x^4-1000*x
^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160
*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+
(-32*x^7+336*x^6-1200*x^5+1000*x^4+3750*x^3-9375*x^2+6250*x)*log(2+x)+32*x^8-336*x^7+1200*x^6-1002*x^5-3749*x^
4+9385*x^3-6250*x^2),x, algorithm="giac")

[Out]

x + log(x - log(16*x^5 - 16*x^4*log(x + 2) - 160*x^4 + 160*x^3*log(x + 2) + 600*x^3 - 600*x^2*log(x + 2) - 100
1*x^2 + 1000*x*log(x + 2) + 625*x - 625*log(x + 2)) + log(16*x^4 - 160*x^3 + 600*x^2 - 1000*x + 625))

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maple [C]  time = 0.35, size = 751, normalized size = 25.90

method	result	size
risch	$x+\ln (\ln (x^5+(-\ln (2+x)-10)x^4+(10\ln (2+x)+\frac{75}{2})x^3+(-\frac{75\ln (2+x)}{2}-\frac{1001}{16})x^2+(\frac{125\ln (2+x)}{2}+\frac{625}{16})x-\frac{625\ln (2+x)}{16})-\frac{i(\pi \mathrm{csgn}\left(\frac{i}{{(x-\frac{5}{2})}^4}\right)\mathrm{csgn}\left(i(-x^5-(-\ln (2+x)-10)x^4-(10\ln (2+x)+\frac{75}{2})x^3-(-\frac{75\ln (2+x)}{2}-\frac{1001}{16})x^2-(\frac{125\ln (2+x)}{2}+\frac{625}{16})x+\frac{625\ln (2+x)}{16})\right)\mathrm{csgn}\left(\frac{i(-x^5-(-\ln (2+x)-10)x^4-(10\ln (2+x)+\frac{75}{2})x^3-(-\frac{75\ln (2+x)}{2}-\frac{1001}{16})x^2-(\frac{125\ln (2+x)}{2}+\frac{625}{16})x+\frac{625\ln (2+x)}{16})}{{(x-\frac{5}{2})}^4}\right)-\pi \mathrm{csgn}\left(\frac{i}{{(x-\frac{5}{2})}^4}\right)\mathrm{csgn}{\left(\frac{i(-x^5-(-\ln (2+x)-10)x^4-(10\ln (2+x)+\frac{75}{2})x^3-(-\frac{75\ln (2+x)}{2}-\frac{1001}{16})x^2-(\frac{125\ln (2+x)}{2}+\frac{625}{16})x+\frac{625\ln (2+x)}{16})}{{(x-\frac{5}{2})}^4}\right)}^2-\pi \mathrm{csgn}{\left(i(x-\frac{5}{2})\right)}^2\mathrm{csgn}\left(i{(x-\frac{5}{2})}^2\right)+2\pi \mathrm{csgn}\left(i(x-\frac{5}{2})\right)\mathrm{csgn}{\left(i{(x-\frac{5}{2})}^2\right)}^2-\pi \mathrm{csgn}\left(i(x-\frac{5}{2})\right)\mathrm{csgn}\left(i{(x-\frac{5}{2})}^2\right)\mathrm{csgn}\left(i{(x-\frac{5}{2})}^3\right)+\pi \mathrm{csgn}\left(i(x-\frac{5}{2})\right)\mathrm{csgn}{\left(i{(x-\frac{5}{2})}^3\right)}^2-\pi \mathrm{csgn}\left(i(x-\frac{5}{2})\right)\mathrm{csgn}\left(i{(x-\frac{5}{2})}^3\right)\mathrm{csgn}\left(i{(x-\frac{5}{2})}^4\right)+\pi \mathrm{csgn}\left(i(x-\frac{5}{2})\right)\mathrm{csgn}{\left(i{(x-\frac{5}{2})}^4\right)}^2-\pi \mathrm{csgn}{\left(i{(x-\frac{5}{2})}^2\right)}^3+\pi \mathrm{csgn}\left(i{(x-\frac{5}{2})}^2\right)\mathrm{csgn}{\left(i{(x-\frac{5}{2})}^3\right)}^2-\pi \mathrm{csgn}{\left(i{(x-\frac{5}{2})}^3\right)}^3+\pi \mathrm{csgn}\left(i{(x-\frac{5}{2})}^3\right)\mathrm{csgn}{\left(i{(x-\frac{5}{2})}^4\right)}^2-\pi \mathrm{csgn}{\left(i{(x-\frac{5}{2})}^4\right)}^3+\pi \mathrm{csgn}\left(i(-x^5-(-\ln (2+x)-10)x^4-(10\ln (2+x)+\frac{75}{2})x^3-(-\frac{75\ln (2+x)}{2}-\frac{1001}{16})x^2-(\frac{125\ln (2+x)}{2}+\frac{625}{16})x+\frac{625\ln (2+x)}{16})\right)\mathrm{csgn}{\left(\frac{i(-x^5-(-\ln (2+x)-10)x^4-(10\ln (2+x)+\frac{75}{2})x^3-(-\frac{75\ln (2+x)}{2}-\frac{1001}{16})x^2-(\frac{125\ln (2+x)}{2}+\frac{625}{16})x+\frac{625\ln (2+x)}{16})}{{(x-\frac{5}{2})}^4}\right)}^2-\pi \mathrm{csgn}{\left(\frac{i(-x^5-(-\ln (2+x)-10)x^4-(10\ln (2+x)+\frac{75}{2})x^3-(-\frac{75\ln (2+x)}{2}-\frac{1001}{16})x^2-(\frac{125\ln (2+x)}{2}+\frac{625}{16})x+\frac{625\ln (2+x)}{16})}{{(x-\frac{5}{2})}^4}\right)}^3-8i\ln (x-\frac{5}{2})-2ix)}{2})$	$751$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^2+9375*x-6250)*ln(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^
3-9385*x^2+6250*x)*ln(((-16*x^4+160*x^3-600*x^2+1000*x-625)*ln(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16
*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+304*x^6-864*x^5-200*x^4+4750*x^3-5625*x^2-3125*x+6250)*ln(2+x)+32*x
^8-304*x^7+832*x^6+566*x^5-6351*x^4+8632*x^3+1867*x^2-9395*x+3125)/(((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^
2+9375*x-6250)*ln(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^3-9385*x^2+6250*x)*ln(((-16*x^4+160*x^3-600*x^2
+1000*x-625)*ln(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+336*
x^6-1200*x^5+1000*x^4+3750*x^3-9375*x^2+6250*x)*ln(2+x)+32*x^8-336*x^7+1200*x^6-1002*x^5-3749*x^4+9385*x^3-625
0*x^2),x,method=_RETURNVERBOSE)

[Out]

x+ln(ln(x^5+(-ln(2+x)-10)*x^4+(10*ln(2+x)+75/2)*x^3+(-75/2*ln(2+x)-1001/16)*x^2+(125/2*ln(2+x)+625/16)*x-625/1
6*ln(2+x))-1/2*I*(Pi*csgn(I/(x-5/2)^4)*csgn(I*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x)-100
1/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*ln(2+x)))*csgn(I/(x-5/2)^4*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)
*x^3-(-75/2*ln(2+x)-1001/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*ln(2+x)))-Pi*csgn(I/(x-5/2)^4)*csgn(I/(x-5/2)
^4*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x)-1001/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*l
n(2+x)))^2-Pi*csgn(I*(x-5/2))^2*csgn(I*(x-5/2)^2)+2*Pi*csgn(I*(x-5/2))*csgn(I*(x-5/2)^2)^2-Pi*csgn(I*(x-5/2))*
csgn(I*(x-5/2)^2)*csgn(I*(x-5/2)^3)+Pi*csgn(I*(x-5/2))*csgn(I*(x-5/2)^3)^2-Pi*csgn(I*(x-5/2))*csgn(I*(x-5/2)^3
)*csgn(I*(x-5/2)^4)+Pi*csgn(I*(x-5/2))*csgn(I*(x-5/2)^4)^2-Pi*csgn(I*(x-5/2)^2)^3+Pi*csgn(I*(x-5/2)^2)*csgn(I*
(x-5/2)^3)^2-Pi*csgn(I*(x-5/2)^3)^3+Pi*csgn(I*(x-5/2)^3)*csgn(I*(x-5/2)^4)^2-Pi*csgn(I*(x-5/2)^4)^3+Pi*csgn(I*
(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x)-1001/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*ln(2
+x)))*csgn(I/(x-5/2)^4*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x)-1001/16)*x^2-(125/2*ln(2+x
)+625/16)*x+625/16*ln(2+x)))^2-Pi*csgn(I/(x-5/2)^4*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x
)-1001/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*ln(2+x)))^3-8*I*ln(x-5/2)-2*I*x))

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maxima [B]  time = 0.73, size = 76, normalized size = 2.62 $$\begin{array}{c}x+\log (-x+\log (16x^5-16x^4(\log (x+2)+10)+40x^3(4\log (x+2)+15)-x^2(600\log (x+2)+1001)+125x(8\log (x+2)+5)-625\log (x+2))-4\log (2x-5))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+
3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+6
25*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+304*x^6-864*x^5-200*x^4+4750*x^3-5625*x^2-3125*x+6250)*log
(2+x)+32*x^8-304*x^7+832*x^6+566*x^5-6351*x^4+8632*x^3+1867*x^2-9395*x+3125)/(((32*x^6-336*x^5+1200*x^4-1000*x
^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160
*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+
(-32*x^7+336*x^6-1200*x^5+1000*x^4+3750*x^3-9375*x^2+6250*x)*log(2+x)+32*x^8-336*x^7+1200*x^6-1002*x^5-3749*x^
4+9385*x^3-6250*x^2),x, algorithm="maxima")

[Out]

x + log(-x + log(16*x^5 - 16*x^4*(log(x + 2) + 10) + 40*x^3*(4*log(x + 2) + 15) - x^2*(600*log(x + 2) + 1001)
+ 125*x*(8*log(x + 2) + 5) - 625*log(x + 2)) - 4*log(2*x - 5))

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mupad [B]  time = 5.16, size = 53, normalized size = 1.83 $$\begin{array}{c}x+\ln (x-\ln \left(\frac{625x-\ln (x+2){(2x-5)}^4-1001x^2+600x^3-160x^4+16x^5}{{(2x-5)}^4}\right))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log((625*x - log(x + 2)*(600*x^2 - 1000*x - 160*x^3 + 16*x^4 + 625) - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x
^5)/(600*x^2 - 1000*x - 160*x^3 + 16*x^4 + 625))*(6250*x - 9385*x^2 + 3749*x^3 + 1002*x^4 - 1200*x^5 + 336*x^6
- 32*x^7 - log(x + 2)*(3750*x^2 - 9375*x + 1000*x^3 - 1200*x^4 + 336*x^5 - 32*x^6 + 6250)) - log(x + 2)*(3125
*x + 5625*x^2 - 4750*x^3 + 200*x^4 + 864*x^5 - 304*x^6 + 32*x^7 - 6250) - 9395*x + 1867*x^2 + 8632*x^3 - 6351*
x^4 + 566*x^5 + 832*x^6 - 304*x^7 + 32*x^8 + 3125)/(log(x + 2)*(6250*x - 9375*x^2 + 3750*x^3 + 1000*x^4 - 1200
*x^5 + 336*x^6 - 32*x^7) + log((625*x - log(x + 2)*(600*x^2 - 1000*x - 160*x^3 + 16*x^4 + 625) - 1001*x^2 + 60
0*x^3 - 160*x^4 + 16*x^5)/(600*x^2 - 1000*x - 160*x^3 + 16*x^4 + 625))*(6250*x - 9385*x^2 + 3749*x^3 + 1002*x^
4 - 1200*x^5 + 336*x^6 - 32*x^7 - log(x + 2)*(3750*x^2 - 9375*x + 1000*x^3 - 1200*x^4 + 336*x^5 - 32*x^6 + 625
0)) - 6250*x^2 + 9385*x^3 - 3749*x^4 - 1002*x^5 + 1200*x^6 - 336*x^7 + 32*x^8),x)

[Out]

x + log(x - log((625*x - log(x + 2)*(2*x - 5)^4 - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5)/(2*x - 5)^4))

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sympy [B]  time = 5.16, size = 75, normalized size = 2.59 $$\begin{array}{c}x+\log (-x+\log \left(\frac{16x^5-160x^4+600x^3-1001x^2+625x+(-16x^4+160x^3-600x^2+1000x-625)\log (x+2)}{16x^4-160x^3+600x^2-1000x+625}\right))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x**6-336*x**5+1200*x**4-1000*x**3-3750*x**2+9375*x-6250)*ln(2+x)-32*x**7+336*x**6-1200*x**5+10
02*x**4+3749*x**3-9385*x**2+6250*x)*ln(((-16*x**4+160*x**3-600*x**2+1000*x-625)*ln(2+x)+16*x**5-160*x**4+600*x
**3-1001*x**2+625*x)/(16*x**4-160*x**3+600*x**2-1000*x+625))+(-32*x**7+304*x**6-864*x**5-200*x**4+4750*x**3-56
25*x**2-3125*x+6250)*ln(2+x)+32*x**8-304*x**7+832*x**6+566*x**5-6351*x**4+8632*x**3+1867*x**2-9395*x+3125)/(((
32*x**6-336*x**5+1200*x**4-1000*x**3-3750*x**2+9375*x-6250)*ln(2+x)-32*x**7+336*x**6-1200*x**5+1002*x**4+3749*
x**3-9385*x**2+6250*x)*ln(((-16*x**4+160*x**3-600*x**2+1000*x-625)*ln(2+x)+16*x**5-160*x**4+600*x**3-1001*x**2
+625*x)/(16*x**4-160*x**3+600*x**2-1000*x+625))+(-32*x**7+336*x**6-1200*x**5+1000*x**4+3750*x**3-9375*x**2+625
0*x)*ln(2+x)+32*x**8-336*x**7+1200*x**6-1002*x**5-3749*x**4+9385*x**3-6250*x**2),x)

[Out]

x + log(-x + log((16*x**5 - 160*x**4 + 600*x**3 - 1001*x**2 + 625*x + (-16*x**4 + 160*x**3 - 600*x**2 + 1000*x
- 625)*log(x + 2))/(16*x**4 - 160*x**3 + 600*x**2 - 1000*x + 625)))

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