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

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

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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 {gather*} -\frac {\log (2) \left (-2 x (2+\log (2)) (13+14 \log (2))+169-\log ^3(2)+192 \log ^2(2)+360 \log (2)\right )}{(1+\log (2))^2 \left (x^2+\log (2)\right )^2}+\frac {-\left (x \left (130+70 \log ^3(2)+249 \log ^2(2)+313 \log (2)\right )\right )+169-2 \log ^4(2)+188 \log ^3(2)+576 \log ^2(2)+551 \log (2)}{(1+\log (2))^3 \left (x^2+\log (2)\right )}+\frac {3 x (2+\log (2)) (13+14 \log (2))}{(1+\log (2))^2 \left (x^2+\log (2)\right )}-\frac {4 (6+\log (128))}{(1-x) (1+\log (2))^3}+\frac {1}{(1-x)^2 (1+\log (2))^2}-\frac {\left (130+70 \log ^3(2)+249 \log ^2(2)+313 \log (2)\right ) \tan ^{-1}\left (\frac {x}{\sqrt {\log (2)}}\right )}{\sqrt {\log (2)} (1+\log (2))^3}+\frac {4 \left (13+7 \log ^3(2)+21 \log ^2(2)+28 \log (2)\right ) \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 {gather*}

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

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Mathematica [B]  time = 0.31, size = 465, normalized size = 18.60 \begin {gather*} -\frac {2 \log ^2(2) \left (\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))\right )+x^3 \left (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))\right )+2 x^2 \log (2) \left (\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))\right )+x^5 \left (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))\right )+x \log (2) \left (-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))\right )+2 x^4 \left (\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))\right )}{4 (-1+x)^2 \log ^2(2) (1+\log (2))^4 \left (x^2+\log (2)\right )^2} \end {gather*}

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 {gather*} -\frac {28 \, x^{5} - 250 \, x^{4} + 390 \, x^{3} + {\left (x^{2} - 2 \, x + 1\right )} \log \relax (2)^{2} - 169 \, x^{2} + 2 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \log \relax (2)}{x^{6} - 2 \, x^{5} + x^{4} + {\left (x^{2} - 2 \, x + 1\right )} \log \relax (2)^{2} + 2 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \log \relax (2)} \end {gather*}

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 {gather*} -\frac {28 \, x^{5} + 2 \, x^{4} \log \relax (2) - 250 \, x^{4} - 4 \, x^{3} \log \relax (2) + x^{2} \log \relax (2)^{2} + 390 \, x^{3} + 2 \, x^{2} \log \relax (2) - 2 \, x \log \relax (2)^{2} - 169 \, x^{2} + \log \relax (2)^{2}}{{\left (x^{3} - x^{2} + x \log \relax (2) - \log \relax (2)\right )}^{2}} \end {gather*}

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

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 {gather*} -\frac {28 \, x^{5} + 2 \, x^{4} {\left (\log \relax (2) - 125\right )} - 2 \, x^{3} {\left (2 \, \log \relax (2) - 195\right )} + {\left (\log \relax (2)^{2} + 2 \, \log \relax (2) - 169\right )} x^{2} - 2 \, x \log \relax (2)^{2} + \log \relax (2)^{2}}{x^{6} - 2 \, x^{5} + x^{4} {\left (2 \, \log \relax (2) + 1\right )} - 4 \, x^{3} \log \relax (2) + {\left (\log \relax (2)^{2} + 2 \, \log \relax (2)\right )} x^{2} - 2 \, x \log \relax (2)^{2} + \log \relax (2)^{2}} \end {gather*}

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 {gather*} \text {Hanged} \end {gather*}

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 {gather*} \frac {- 28 x^{5} + x^{4} \left (250 - 2 \log {\relax (2 )}\right ) + x^{3} \left (-390 + 4 \log {\relax (2 )}\right ) + x^{2} \left (- 2 \log {\relax (2 )} - \log {\relax (2 )}^{2} + 169\right ) + 2 x \log {\relax (2 )}^{2} - \log {\relax (2 )}^{2}}{x^{6} - 2 x^{5} + x^{4} \left (1 + 2 \log {\relax (2 )}\right ) - 4 x^{3} \log {\relax (2 )} + x^{2} \left (\log {\relax (2 )}^{2} + 2 \log {\relax (2 )}\right ) - 2 x \log {\relax (2 )}^{2} + \log {\relax (2 )}^{2}} \end {gather*}

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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