3.85.12 $\int \frac{338x^3-1066x^4+1170x^5-472x^6+28x^7+(-338x+1170x^2-1394x^3+652x^4-96x^5+4x^6)\log (2)}{-x^6+3x^7-3x^8+x^9+(-3x^4+9x^5-9x^6+3x^7)\log (2)+(-3x^2+9x^3-9x^4+3x^5){\log }^2(2)+(-1+3x-3x^2+x^3){\log }^3(2)}dx$

Optimal. Leaf size=25 $$\frac{x^2{(-13+x-\frac{x}{-1+x})}^2}{{(x^2+\log (2))}^2}$$

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Rubi [B]  time = 0.40, antiderivative size = 285, normalized size of antiderivative = 11.40, number of steps used = 8, number of rules used = 4, integrand size = 148, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.027, Rules used = {2074, 203, 639, 199} $$\begin{array}{c}-\frac{\log (2)(-2x(2+\log (2))(13+14\log (2))+169-{\log }^3(2)+192{\log }^2(2)+360\log (2))}{(1+\log (2){)}^2{(x^2+\log (2))}^2}+\frac{-\left(x(130+70{\log }^3(2)+249{\log }^2(2)+313\log (2))\right)+169-2{\log }^4(2)+188{\log }^3(2)+576{\log }^2(2)+551\log (2)}{(1+\log (2){)}^3(x^2+\log (2))}+\frac{3x(2+\log (2))(13+14\log (2))}{(1+\log (2){)}^2(x^2+\log (2))}-\frac{4(6+\log (128))}{(1-x)(1+\log (2){)}^3}+\frac{1}{(1-x{)}^2(1+\log (2){)}^2}-\frac{(130+70{\log }^3(2)+249{\log }^2(2)+313\log (2)){\tan }^{-1}\left(\frac{x}{\sqrt{\log (2)}}\right)}{\sqrt{\log (2)}(1+\log (2){)}^3}+\frac{4(13+7{\log }^3(2)+21{\log }^2(2)+28\log (2)){\tan }^{-1}\left(\frac{x}{\sqrt{\log (2)}}\right)}{\sqrt{\log (2)}(1+\log (2){)}^3}+\frac{3(2+\log (2))(13+14\log (2)){\tan }^{-1}\left(\frac{x}{\sqrt{\log (2)}}\right)}{\sqrt{\log (2)}(1+\log (2){)}^2}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(338*x^3 - 1066*x^4 + 1170*x^5 - 472*x^6 + 28*x^7 + (-338*x + 1170*x^2 - 1394*x^3 + 652*x^4 - 96*x^5 + 4*x
^6)*Log[2])/(-x^6 + 3*x^7 - 3*x^8 + x^9 + (-3*x^4 + 9*x^5 - 9*x^6 + 3*x^7)*Log[2] + (-3*x^2 + 9*x^3 - 9*x^4 +
3*x^5)*Log[2]^2 + (-1 + 3*x - 3*x^2 + x^3)*Log[2]^3),x]

[Out]

1/((1 - x)^2*(1 + Log[2])^2) + (3*ArcTan[x/Sqrt[Log[2]]]*(2 + Log[2])*(13 + 14*Log[2]))/(Sqrt[Log[2]]*(1 + Log
[2])^2) + (3*x*(2 + Log[2])*(13 + 14*Log[2]))/((1 + Log[2])^2*(x^2 + Log[2])) + (4*ArcTan[x/Sqrt[Log[2]]]*(13
+ 28*Log[2] + 21*Log[2]^2 + 7*Log[2]^3))/(Sqrt[Log[2]]*(1 + Log[2])^3) - (ArcTan[x/Sqrt[Log[2]]]*(130 + 313*Lo
g[2] + 249*Log[2]^2 + 70*Log[2]^3))/(Sqrt[Log[2]]*(1 + Log[2])^3) - (Log[2]*(169 + 360*Log[2] + 192*Log[2]^2 -
Log[2]^3 - 2*x*(2 + Log[2])*(13 + 14*Log[2])))/((1 + Log[2])^2*(x^2 + Log[2])^2) + (169 + 551*Log[2] + 576*Lo
g[2]^2 + 188*Log[2]^3 - 2*Log[2]^4 - x*(130 + 313*Log[2] + 249*Log[2]^2 + 70*Log[2]^3))/((1 + Log[2])^3*(x^2 +
Log[2])) - (4*(6 + Log[128]))/((1 - x)*(1 + Log[2])^3)

Rule 199

Int[((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> -Simp[(x*(a + b*x^n)^(p + 1))/(a*n*(p + 1)), x] + Dist[(n*(p +
1) + 1)/(a*n*(p + 1)), Int[(a + b*x^n)^(p + 1), x], x] /; FreeQ[{a, b}, x] && IGtQ[n, 0] && LtQ[p, -1] && (In
tegerQ[2*p] || (n == 2 && IntegerQ[4*p]) || (n == 2 && IntegerQ[3*p]) || Denominator[p + 1/n] < Denominator[p]
)

Rule 203

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTan[(Rt[b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[b, 2]), x] /;
FreeQ[{a, b}, x] && PosQ[a/b] && (GtQ[a, 0] || GtQ[b, 0])

Rule 639

Int[((d_) + (e_.)*(x_))*((a_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((a*e - c*d*x)*(a + c*x^2)^(p + 1))/(2*a
*c*(p + 1)), x] + Dist[(d*(2*p + 3))/(2*a*(p + 1)), Int[(a + c*x^2)^(p + 1), x], x] /; FreeQ[{a, c, d, e}, x]
&& LtQ[p, -1] && NeQ[p, -3/2]

Rule 2074

Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /;  !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (-\frac{2}{(-1+x{)}^3(1+\log (2){)}^2}+\frac{4(13+28\log (2)+21{\log }^2(2)+7{\log }^3(2))}{(1+\log (2){)}^3(x^2+\log (2))}+\frac{4\log (2)(2\log (2)(2+\log (2))(13+14\log (2))+x(169+360\log (2)+192{\log }^2(2)-{\log }^3(2)))}{(1+\log (2){)}^2{(x^2+\log (2))}^3}+\frac{2(-\log (2)(130+313\log (2)+249{\log }^2(2)+70{\log }^3(2))-x(169+551\log (2)+576{\log }^2(2)+188{\log }^3(2)-2{\log }^4(2)))}{(1+\log (2){)}^3{(x^2+\log (2))}^2}-\frac{4(6+\log (128))}{(-1+x{)}^2(1+\log (2){)}^3})dx\\ & =\frac{1}{(1-x{)}^2(1+\log (2){)}^2}-\frac{4(6+\log (128))}{(1-x)(1+\log (2){)}^3}+\frac{2\int \frac{-\log (2)(130+313\log (2)+249{\log }^2(2)+70{\log }^3(2))-x(169+551\log (2)+576{\log }^2(2)+188{\log }^3(2)-2{\log }^4(2))}{{(x^2+\log (2))}^2}dx}{(1+\log (2){)}^3}+\frac{(4\log (2))\int \frac{2\log (2)(2+\log (2))(13+14\log (2))+x(169+360\log (2)+192{\log }^2(2)-{\log }^3(2))}{{(x^2+\log (2))}^3}dx}{(1+\log (2){)}^2}+\frac{\left(4(13+28\log (2)+21{\log }^2(2)+7{\log }^3(2))\right)\int \frac{1}{x^2+\log (2)}dx}{(1+\log (2){)}^3}\\ & =\frac{1}{(1-x{)}^2(1+\log (2){)}^2}+\frac{4{\tan }^{-1}\left(\frac{x}{\sqrt{\log (2)}}\right)(13+28\log (2)+21{\log }^2(2)+7{\log }^3(2))}{\sqrt{\log (2)}(1+\log (2){)}^3}-\frac{\log (2)(169+360\log (2)+192{\log }^2(2)-{\log }^3(2)-2x(2+\log (2))(13+14\log (2)))}{(1+\log (2){)}^2{(x^2+\log (2))}^2}+\frac{169+551\log (2)+576{\log }^2(2)+188{\log }^3(2)-2{\log }^4(2)-x(130+313\log (2)+249{\log }^2(2)+70{\log }^3(2))}{(1+\log (2){)}^3(x^2+\log (2))}-\frac{4(6+\log (128))}{(1-x)(1+\log (2){)}^3}+\frac{(6\log (2)(2+\log (2))(13+14\log (2)))\int \frac{1}{{(x^2+\log (2))}^2}dx}{(1+\log (2){)}^2}-\frac{(130+313\log (2)+249{\log }^2(2)+70{\log }^3(2))\int \frac{1}{x^2+\log (2)}dx}{(1+\log (2){)}^3}\\ & =\frac{1}{(1-x{)}^2(1+\log (2){)}^2}+\frac{3x(2+\log (2))(13+14\log (2))}{(1+\log (2){)}^2(x^2+\log (2))}+\frac{4{\tan }^{-1}\left(\frac{x}{\sqrt{\log (2)}}\right)(13+28\log (2)+21{\log }^2(2)+7{\log }^3(2))}{\sqrt{\log (2)}(1+\log (2){)}^3}-\frac{{\tan }^{-1}\left(\frac{x}{\sqrt{\log (2)}}\right)(130+313\log (2)+249{\log }^2(2)+70{\log }^3(2))}{\sqrt{\log (2)}(1+\log (2){)}^3}-\frac{\log (2)(169+360\log (2)+192{\log }^2(2)-{\log }^3(2)-2x(2+\log (2))(13+14\log (2)))}{(1+\log (2){)}^2{(x^2+\log (2))}^2}+\frac{169+551\log (2)+576{\log }^2(2)+188{\log }^3(2)-2{\log }^4(2)-x(130+313\log (2)+249{\log }^2(2)+70{\log }^3(2))}{(1+\log (2){)}^3(x^2+\log (2))}-\frac{4(6+\log (128))}{(1-x)(1+\log (2){)}^3}+\frac{(3(2+\log (2))(13+14\log (2)))\int \frac{1}{x^2+\log (2)}dx}{(1+\log (2){)}^2}\\ & =\frac{1}{(1-x{)}^2(1+\log (2){)}^2}+\frac{3{\tan }^{-1}\left(\frac{x}{\sqrt{\log (2)}}\right)(2+\log (2))(13+14\log (2))}{\sqrt{\log (2)}(1+\log (2){)}^2}+\frac{3x(2+\log (2))(13+14\log (2))}{(1+\log (2){)}^2(x^2+\log (2))}+\frac{4{\tan }^{-1}\left(\frac{x}{\sqrt{\log (2)}}\right)(13+28\log (2)+21{\log }^2(2)+7{\log }^3(2))}{\sqrt{\log (2)}(1+\log (2){)}^3}-\frac{{\tan }^{-1}\left(\frac{x}{\sqrt{\log (2)}}\right)(130+313\log (2)+249{\log }^2(2)+70{\log }^3(2))}{\sqrt{\log (2)}(1+\log (2){)}^3}-\frac{\log (2)(169+360\log (2)+192{\log }^2(2)-{\log }^3(2)-2x(2+\log (2))(13+14\log (2)))}{(1+\log (2){)}^2{(x^2+\log (2))}^2}+\frac{169+551\log (2)+576{\log }^2(2)+188{\log }^3(2)-2{\log }^4(2)-x(130+313\log (2)+249{\log }^2(2)+70{\log }^3(2))}{(1+\log (2){)}^3(x^2+\log (2))}-\frac{4(6+\log (128))}{(1-x)(1+\log (2){)}^3}\end{array}\end{array}$$

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Mathematica [B]  time = 0.31, size = 465, normalized size = 18.60 $$\begin{array}{c}-\frac{2{\log }^2(2)({\log }^3(2)(1652-374\log (4))+{\log }^4(2)(760-22\log (4))+360\log (4)+{\log }^5(2)(52+\log (4))+9\log (2)(-80+9\log (4))-2{\log }^2(2)(80+411\log (4)))+x^3(24{\log }^7(2)+\log (2)(3024-2841\log (4))+{\log }^6(2)(1222-20\log (4))-1512\log (4)+34{\log }^2(2)(213+94\log (4))+{\log }^5(2)(-448+137\log (4))+16{\log }^4(2)(-437+206\log (4))+8{\log }^3(2)(-21+1018\log (4)))+2x^2\log (2)({\log }^3(2)(10494-3313\log (4))+{\log }^4(2)(5306-247\log (4))-8{\log }^5(2)(-23+\log (4))+2520\log (4)+{\log }^6(2)(28+\log (4))+\log (2)(-5378+543\log (4))-2{\log }^2(2)(1217+3126\log (4)))+x^5(88{\log }^6(2)+\log (2)(3024-321\log (4))-1512\log (4)+2{\log }^5(2)(53+6\log (4))+9{\log }^4(2)(-374+19\log (4))+{\log }^3(2)(-7094+2019\log (4))+{\log }^2(2)(754+3771\log (4)))+x\log (2)(-2520\log (4)-4{\log }^6(2)(46+\log (4))-15\log (2)(-336+89\log (4))+{\log }^4(2)(-10778+1325\log (4))+3{\log }^2(2)(890+2043\log (4))+{\log }^3(2)(-12266+5373\log (4))+38{\log }^5(2)(-71+\log (16)))+2x^4({\log }^3(2)(5542-2011\log (4))+2{\log }^6(2)(-238+\log (4))+1512\log (4)-3{\log }^4(2)(-346+53\log (4))+\log (2)(-3024+321\log (4))-{\log }^2(2)(1142+3769\log (4))-2{\log }^5(2)(829+\log (16)))}{4(-1+x{)}^2{\log }^2(2)(1+\log (2){)}^4{(x^2+\log (2))}^2}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(338*x^3 - 1066*x^4 + 1170*x^5 - 472*x^6 + 28*x^7 + (-338*x + 1170*x^2 - 1394*x^3 + 652*x^4 - 96*x^5
+ 4*x^6)*Log[2])/(-x^6 + 3*x^7 - 3*x^8 + x^9 + (-3*x^4 + 9*x^5 - 9*x^6 + 3*x^7)*Log[2] + (-3*x^2 + 9*x^3 - 9*
x^4 + 3*x^5)*Log[2]^2 + (-1 + 3*x - 3*x^2 + x^3)*Log[2]^3),x]

[Out]

-1/4*(2*Log[2]^2*(Log[2]^3*(1652 - 374*Log[4]) + Log[2]^4*(760 - 22*Log[4]) + 360*Log[4] + Log[2]^5*(52 + Log[
4]) + 9*Log[2]*(-80 + 9*Log[4]) - 2*Log[2]^2*(80 + 411*Log[4])) + x^3*(24*Log[2]^7 + Log[2]*(3024 - 2841*Log[4
]) + Log[2]^6*(1222 - 20*Log[4]) - 1512*Log[4] + 34*Log[2]^2*(213 + 94*Log[4]) + Log[2]^5*(-448 + 137*Log[4])
+ 16*Log[2]^4*(-437 + 206*Log[4]) + 8*Log[2]^3*(-21 + 1018*Log[4])) + 2*x^2*Log[2]*(Log[2]^3*(10494 - 3313*Log
[4]) + Log[2]^4*(5306 - 247*Log[4]) - 8*Log[2]^5*(-23 + Log[4]) + 2520*Log[4] + Log[2]^6*(28 + Log[4]) + Log[2
]*(-5378 + 543*Log[4]) - 2*Log[2]^2*(1217 + 3126*Log[4])) + x^5*(88*Log[2]^6 + Log[2]*(3024 - 321*Log[4]) - 15
12*Log[4] + 2*Log[2]^5*(53 + 6*Log[4]) + 9*Log[2]^4*(-374 + 19*Log[4]) + Log[2]^3*(-7094 + 2019*Log[4]) + Log[
2]^2*(754 + 3771*Log[4])) + x*Log[2]*(-2520*Log[4] - 4*Log[2]^6*(46 + Log[4]) - 15*Log[2]*(-336 + 89*Log[4]) +
Log[2]^4*(-10778 + 1325*Log[4]) + 3*Log[2]^2*(890 + 2043*Log[4]) + Log[2]^3*(-12266 + 5373*Log[4]) + 38*Log[2
]^5*(-71 + Log[16])) + 2*x^4*(Log[2]^3*(5542 - 2011*Log[4]) + 2*Log[2]^6*(-238 + Log[4]) + 1512*Log[4] - 3*Log
[2]^4*(-346 + 53*Log[4]) + Log[2]*(-3024 + 321*Log[4]) - Log[2]^2*(1142 + 3769*Log[4]) - 2*Log[2]^5*(829 + Log
[16])))/((-1 + x)^2*Log[2]^2*(1 + Log[2])^4*(x^2 + Log[2])^2)

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fricas [B]  time = 0.59, size = 95, normalized size = 3.80 $$\begin{array}{c}-\frac{28x^5-250x^4+390x^3+(x^2-2x+1)\log (2{)}^2-169x^2+2(x^4-2x^3+x^2)\log (2)}{x^6-2x^5+x^4+(x^2-2x+1)\log (2{)}^2+2(x^4-2x^3+x^2)\log (2)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-96*x^5+652*x^4-1394*x^3+1170*x^2-338*x)*log(2)+28*x^7-472*x^6+1170*x^5-1066*x^4+338*x^3)/((x
^3-3*x^2+3*x-1)*log(2)^3+(3*x^5-9*x^4+9*x^3-3*x^2)*log(2)^2+(3*x^7-9*x^6+9*x^5-3*x^4)*log(2)+x^9-3*x^8+3*x^7-x
^6),x, algorithm="fricas")

[Out]

-(28*x^5 - 250*x^4 + 390*x^3 + (x^2 - 2*x + 1)*log(2)^2 - 169*x^2 + 2*(x^4 - 2*x^3 + x^2)*log(2))/(x^6 - 2*x^5
+ x^4 + (x^2 - 2*x + 1)*log(2)^2 + 2*(x^4 - 2*x^3 + x^2)*log(2))

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giac [B]  time = 0.25, size = 82, normalized size = 3.28 $$\begin{array}{c}-\frac{28x^5+2x^4\log (2)-250x^4-4x^3\log (2)+x^2\log (2{)}^2+390x^3+2x^2\log (2)-2x\log (2{)}^2-169x^2+\log (2{)}^2}{{(x^3-x^2+x\log (2)-\log (2))}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-96*x^5+652*x^4-1394*x^3+1170*x^2-338*x)*log(2)+28*x^7-472*x^6+1170*x^5-1066*x^4+338*x^3)/((x
^3-3*x^2+3*x-1)*log(2)^3+(3*x^5-9*x^4+9*x^3-3*x^2)*log(2)^2+(3*x^7-9*x^6+9*x^5-3*x^4)*log(2)+x^9-3*x^8+3*x^7-x
^6),x, algorithm="giac")

[Out]

-(28*x^5 + 2*x^4*log(2) - 250*x^4 - 4*x^3*log(2) + x^2*log(2)^2 + 390*x^3 + 2*x^2*log(2) - 2*x*log(2)^2 - 169*
x^2 + log(2)^2)/(x^3 - x^2 + x*log(2) - log(2))^2

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maple [B]  time = 0.22, size = 70, normalized size = 2.80

method	result	size
norman	$\frac{-28x^5+2x\ln (2{)}^2+(4\ln (2)-390)x^3+(-2\ln (2)+250)x^4+(-\ln (2{)}^2-2\ln (2)+169)x^2-\ln (2{)}^2}{{(x-1)}^2{(\ln (2)+x^2)}^2}$	$70$
risch	$\frac{-28x^5+2x\ln (2{)}^2+(4\ln (2)-390)x^3+(-2\ln (2)+250)x^4+(-\ln (2{)}^2-2\ln (2)+169)x^2-\ln (2{)}^2}{x^6+2x^4\ln (2)-2x^5+x^2\ln (2{)}^2-4x^3\ln (2)+x^4-2x\ln (2{)}^2+2x^2\ln (2)+\ln (2{)}^2}$	$111$
gosper	$-\frac{2x^4\ln (2)+28x^5+x^2\ln (2{)}^2-4x^3\ln (2)-250x^4-2x\ln (2{)}^2+2x^2\ln (2)+390x^3+\ln (2{)}^2-169x^2}{x^6+2x^4\ln (2)-2x^5+x^2\ln (2{)}^2-4x^3\ln (2)+x^4-2x\ln (2{)}^2+2x^2\ln (2)+\ln (2{)}^2}$	$118$
default	$\frac{2(-14\ln (2{)}^3-42\ln (2{)}^2-56\ln (2)-26)x^3+2(-\ln (2{)}^4+94\ln (2{)}^3+288\ln (2{)}^2+\frac{551\ln (2)}{2}+\frac{169}{2})x^2+2(13\ln (2{)}^3+11\ln (2{)}^2)x-\ln (2{)}^5-3\ln (2{)}^4+24\ln (2{)}^3+22\ln (2{)}^2}{{(\ln (2)+x^2)}^2{(1+\ln (2))}^3}-\frac{2(-14\ln (2)-12)}{{(1+\ln (2))}^3(x-1)}+\frac{1}{{(1+\ln (2))}^2{(x-1)}^2}$	$139$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^6-96*x^5+652*x^4-1394*x^3+1170*x^2-338*x)*ln(2)+28*x^7-472*x^6+1170*x^5-1066*x^4+338*x^3)/((x^3-3*x^
2+3*x-1)*ln(2)^3+(3*x^5-9*x^4+9*x^3-3*x^2)*ln(2)^2+(3*x^7-9*x^6+9*x^5-3*x^4)*ln(2)+x^9-3*x^8+3*x^7-x^6),x,meth
od=_RETURNVERBOSE)

[Out]

(-28*x^5+2*x*ln(2)^2+(4*ln(2)-390)*x^3+(-2*ln(2)+250)*x^4+(-ln(2)^2-2*ln(2)+169)*x^2-ln(2)^2)/(x-1)^2/(ln(2)+x
^2)^2

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maxima [B]  time = 0.37, size = 105, normalized size = 4.20 $$\begin{array}{c}-\frac{28x^5+2x^4(\log (2)-125)-2x^3(2\log (2)-195)+(\log (2{)}^2+2\log (2)-169)x^2-2x\log (2{)}^2+\log (2{)}^2}{x^6-2x^5+x^4(2\log (2)+1)-4x^3\log (2)+(\log (2{)}^2+2\log (2))x^2-2x\log (2{)}^2+\log (2{)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-96*x^5+652*x^4-1394*x^3+1170*x^2-338*x)*log(2)+28*x^7-472*x^6+1170*x^5-1066*x^4+338*x^3)/((x
^3-3*x^2+3*x-1)*log(2)^3+(3*x^5-9*x^4+9*x^3-3*x^2)*log(2)^2+(3*x^7-9*x^6+9*x^5-3*x^4)*log(2)+x^9-3*x^8+3*x^7-x
^6),x, algorithm="maxima")

[Out]

-(28*x^5 + 2*x^4*(log(2) - 125) - 2*x^3*(2*log(2) - 195) + (log(2)^2 + 2*log(2) - 169)*x^2 - 2*x*log(2)^2 + lo
g(2)^2)/(x^6 - 2*x^5 + x^4*(2*log(2) + 1) - 4*x^3*log(2) + (log(2)^2 + 2*log(2))*x^2 - 2*x*log(2)^2 + log(2)^2
)

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mupad [F(-1)]  time = 0.00, size = -1, normalized size = -0.04 $$\begin{array}{c}\text{Hanged}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(2)*(338*x - 1170*x^2 + 1394*x^3 - 652*x^4 + 96*x^5 - 4*x^6) - 338*x^3 + 1066*x^4 - 1170*x^5 + 472*x^6
- 28*x^7)/(log(2)*(3*x^4 - 9*x^5 + 9*x^6 - 3*x^7) + log(2)^2*(3*x^2 - 9*x^3 + 9*x^4 - 3*x^5) - log(2)^3*(3*x
- 3*x^2 + x^3 - 1) + x^6 - 3*x^7 + 3*x^8 - x^9),x)

[Out]

\text{Hanged}

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sympy [B]  time = 8.40, size = 107, normalized size = 4.28 $$\begin{array}{c}\frac{-28x^5+x^4(250-2\log (2))+x^3(-390+4\log (2))+x^2(-2\log (2)-\log {(2)}^2+169)+2x\log {(2)}^2-\log {(2)}^2}{x^6-2x^5+x^4(1+2\log (2))-4x^3\log (2)+x^2(\log {(2)}^2+2\log (2))-2x\log {(2)}^2+\log {(2)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**6-96*x**5+652*x**4-1394*x**3+1170*x**2-338*x)*ln(2)+28*x**7-472*x**6+1170*x**5-1066*x**4+338*
x**3)/((x**3-3*x**2+3*x-1)*ln(2)**3+(3*x**5-9*x**4+9*x**3-3*x**2)*ln(2)**2+(3*x**7-9*x**6+9*x**5-3*x**4)*ln(2)
+x**9-3*x**8+3*x**7-x**6),x)

[Out]

(-28*x**5 + x**4*(250 - 2*log(2)) + x**3*(-390 + 4*log(2)) + x**2*(-2*log(2) - log(2)**2 + 169) + 2*x*log(2)**
2 - log(2)**2)/(x**6 - 2*x**5 + x**4*(1 + 2*log(2)) - 4*x**3*log(2) + x**2*(log(2)**2 + 2*log(2)) - 2*x*log(2)
**2 + log(2)**2)

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