3.96.82 \(\int \frac {-16 x-16 x^2 \log (2)+(-20+20 x-4 x^3) \log ^2(2)+(16 x \log (2)+8 x^2 \log ^2(2)) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+(-80 x+84 x^2-32 x^3+4 x^4) \log (2)+(25 x-40 x^2+26 x^3-8 x^4+x^5) \log ^2(2)+((-64 x+32 x^2-4 x^3) \log (2)+(40 x-42 x^2+16 x^3-2 x^4) \log ^2(2)) \log (-x)+(16 x-8 x^2+x^3) \log ^2(2) \log ^2(-x)} \, dx\)

Optimal. Leaf size=25 \[ \frac {4}{-4+x+\frac {5}{x+\frac {2}{\log (2)}-\log (-x)}} \]

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Rubi [F]  time = 4.81, 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 {gather*} \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-16*x - 16*x^2*Log[2] + (-20 + 20*x - 4*x^3)*Log[2]^2 + (16*x*Log[2] + 8*x^2*Log[2]^2)*Log[-x] - 4*x*Log[
2]^2*Log[-x]^2)/(64*x - 32*x^2 + 4*x^3 + (-80*x + 84*x^2 - 32*x^3 + 4*x^4)*Log[2] + (25*x - 40*x^2 + 26*x^3 -
8*x^4 + x^5)*Log[2]^2 + ((-64*x + 32*x^2 - 4*x^3)*Log[2] + (40*x - 42*x^2 + 16*x^3 - 2*x^4)*Log[2]^2)*Log[-x]
+ (16*x - 8*x^2 + x^3)*Log[2]^2*Log[-x]^2),x]

[Out]

(4*Log[2])/(x*Log[2] - Log[16]) - (4*(11*Log[2]^4 - 8*Log[2]^3*Log[16] - Log[4]*Log[16]^2 + Log[2]^2*Log[16]*(
8 + Log[16]))*Defer[Int][(8*(1 - (5*Log[2])/8) - x^2*Log[2] - 2*x*(1 - Log[4]) + x*Log[2]*Log[-x] - Log[16]*Lo
g[-x])^(-2), x])/Log[2]^2 - 20*Log[2]^2*Defer[Int][1/(x*(8*(1 - (5*Log[2])/8) - x^2*Log[2] - 2*x*(1 - Log[4])
+ x*Log[2]*Log[-x] - Log[16]*Log[-x])^2), x] - (4*(25*Log[2]^6 + Log[2]*Log[16]^4 - Log[4]*Log[16]^4 - 40*Log[
2]^5*(2 + Log[16]) - 8*Log[2]^3*Log[16]*(2 + Log[16])^2 + Log[2]^2*Log[16]^2*(4 + 8*Log[16] + Log[16]^2) + Log
[2]^4*(64 + 84*Log[16] + 26*Log[16]^2))*Defer[Int][1/((x*Log[2] - Log[16])^2*(8*(1 - (5*Log[2])/8) - x^2*Log[2
] - 2*x*(1 - Log[4]) + x*Log[2]*Log[-x] - Log[16]*Log[-x])^2), x])/Log[2]^2 + (4*(40*Log[2]^5 - Log[2]*Log[16]
^3 + Log[16]^4 + 16*Log[2]^3*Log[16]*(2 + Log[16]) - 2*Log[2]^2*Log[16]^2*(8 + Log[16]) - 2*Log[2]^4*(32 + 21*
Log[16]))*Defer[Int][1/((x*Log[2] - Log[16])*(8*(1 - (5*Log[2])/8) - x^2*Log[2] - 2*x*(1 - Log[4]) + x*Log[2]*
Log[-x] - Log[16]*Log[-x])^2), x])/Log[2]^2 + 8*Log[2]^2*Log[32]*Defer[Int][1/((x*Log[2] - Log[16])^2*(-8*(1 -
(5*Log[2])/8) + x^2*Log[2] + 2*x*(1 - Log[4]) - x*Log[2]*Log[-x] + Log[16]*Log[-x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (-5 \log ^2(2)-x^3 \log ^2(2)-x \left (4-5 \log ^2(2)\right )-x^2 \log (16)+2 x \log (2) (2+x \log (2)) \log (-x)-x \log ^2(2) \log ^2(-x)\right )}{x \left (x (2-4 \log (2))-8 \left (1-\frac {5 \log (2)}{8}\right )+x^2 \log (2)+(-x \log (2)+\log (16)) \log (-x)\right )^2} \, dx\\ &=4 \int \frac {-5 \log ^2(2)-x^3 \log ^2(2)-x \left (4-5 \log ^2(2)\right )-x^2 \log (16)+2 x \log (2) (2+x \log (2)) \log (-x)-x \log ^2(2) \log ^2(-x)}{x \left (x (2-4 \log (2))-8 \left (1-\frac {5 \log (2)}{8}\right )+x^2 \log (2)+(-x \log (2)+\log (16)) \log (-x)\right )^2} \, dx\\ &=4 \int \left (-\frac {\log ^2(2)}{(x \log (2)-\log (16))^2}+\frac {-5 \log ^2(2) \log ^2(16)-x^3 \left (11 \log ^4(2)-8 \log ^3(2) \log (16)-\log (4) \log ^2(16)+\log ^2(2) \log (16) (8+\log (16))\right )+x^2 \left (35 \log ^4(2)+32 \log ^2(2) \log (16)-\log ^3(16)-4 \log ^3(2) (16+5 \log (16))\right )-x \left (25 \log ^4(2)-32 \log (2) \log (16)+4 \log ^2(16)-10 \log ^3(2) (8+\log (16))+\log ^2(2) \left (64+20 \log (16)-5 \log ^2(16)\right )\right )}{x (x \log (2)-\log (16))^2 \left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2}+\frac {2 \log ^2(2) \log (32)}{(x \log (2)-\log (16))^2 \left (-8 \left (1-\frac {5 \log (2)}{8}\right )+x^2 \log (2)+2 x (1-\log (4))-x \log (2) \log (-x)+\log (16) \log (-x)\right )}\right ) \, dx\\ &=\frac {4 \log (2)}{x \log (2)-\log (16)}+4 \int \frac {-5 \log ^2(2) \log ^2(16)-x^3 \left (11 \log ^4(2)-8 \log ^3(2) \log (16)-\log (4) \log ^2(16)+\log ^2(2) \log (16) (8+\log (16))\right )+x^2 \left (35 \log ^4(2)+32 \log ^2(2) \log (16)-\log ^3(16)-4 \log ^3(2) (16+5 \log (16))\right )-x \left (25 \log ^4(2)-32 \log (2) \log (16)+4 \log ^2(16)-10 \log ^3(2) (8+\log (16))+\log ^2(2) \left (64+20 \log (16)-5 \log ^2(16)\right )\right )}{x (x \log (2)-\log (16))^2 \left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2} \, dx+\left (8 \log ^2(2) \log (32)\right ) \int \frac {1}{(x \log (2)-\log (16))^2 \left (-8 \left (1-\frac {5 \log (2)}{8}\right )+x^2 \log (2)+2 x (1-\log (4))-x \log (2) \log (-x)+\log (16) \log (-x)\right )} \, dx\\ &=\frac {4 \log (2)}{x \log (2)-\log (16)}+4 \int \left (-\frac {5 \log ^2(2)}{x \left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2}+\frac {-11 \log ^4(2)+8 \log ^3(2) \log (16)+\log (4) \log ^2(16)-\log ^2(2) \log (16) (8+\log (16))}{\log ^2(2) \left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2}+\frac {40 \log ^5(2)-\log (2) \log ^3(16)+\log ^4(16)+16 \log ^3(2) \log (16) (2+\log (16))-2 \log ^2(2) \log ^2(16) (8+\log (16))-2 \log ^4(2) (32+21 \log (16))}{\log ^2(2) (x \log (2)-\log (16)) \left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2}+\frac {-25 \log ^6(2)-\log (2) \log ^4(16)+\log (4) \log ^4(16)+40 \log ^5(2) (2+\log (16))+8 \log ^3(2) \log (16) (2+\log (16))^2-\log ^2(2) \log ^2(16) \left (4+8 \log (16)+\log ^2(16)\right )-2 \log ^4(2) \left (32+42 \log (16)+13 \log ^2(16)\right )}{\log ^2(2) (x \log (2)-\log (16))^2 \left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2}\right ) \, dx+\left (8 \log ^2(2) \log (32)\right ) \int \frac {1}{(x \log (2)-\log (16))^2 \left (-8 \left (1-\frac {5 \log (2)}{8}\right )+x^2 \log (2)+2 x (1-\log (4))-x \log (2) \log (-x)+\log (16) \log (-x)\right )} \, dx\\ &=\frac {4 \log (2)}{x \log (2)-\log (16)}-\left (20 \log ^2(2)\right ) \int \frac {1}{x \left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2} \, dx+\frac {\left (4 \left (-11 \log ^4(2)+8 \log ^3(2) \log (16)+\log (4) \log ^2(16)-\log ^2(2) \log (16) (8+\log (16))\right )\right ) \int \frac {1}{\left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2} \, dx}{\log ^2(2)}+\frac {\left (4 \left (40 \log ^5(2)-\log (2) \log ^3(16)+\log ^4(16)+16 \log ^3(2) \log (16) (2+\log (16))-2 \log ^2(2) \log ^2(16) (8+\log (16))-2 \log ^4(2) (32+21 \log (16))\right )\right ) \int \frac {1}{(x \log (2)-\log (16)) \left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2} \, dx}{\log ^2(2)}-\frac {\left (4 \left (25 \log ^6(2)+\log (2) \log ^4(16)-\log (4) \log ^4(16)-40 \log ^5(2) (2+\log (16))-8 \log ^3(2) \log (16) (2+\log (16))^2+\log ^2(2) \log ^2(16) \left (4+8 \log (16)+\log ^2(16)\right )+\log ^4(2) \left (64+84 \log (16)+26 \log ^2(16)\right )\right )\right ) \int \frac {1}{(x \log (2)-\log (16))^2 \left (8 \left (1-\frac {5 \log (2)}{8}\right )-x^2 \log (2)-2 x (1-\log (4))+x \log (2) \log (-x)-\log (16) \log (-x)\right )^2} \, dx}{\log ^2(2)}+\left (8 \log ^2(2) \log (32)\right ) \int \frac {1}{(x \log (2)-\log (16))^2 \left (-8 \left (1-\frac {5 \log (2)}{8}\right )+x^2 \log (2)+2 x (1-\log (4))-x \log (2) \log (-x)+\log (16) \log (-x)\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.23, size = 228, normalized size = 9.12 \begin {gather*} -\frac {4 \left (-x^4 \log ^3(2)+x^3 \log (2) \left (5 \log ^2(2)-\log (4)+\log (2) \log (16)\right )+x^2 \left (-15 \log ^3(2)-\log ^2(2) (-2+\log (16))+\log ^2(16)\right )-\log (2) \log (16) \log (32)+\log (16) \log (256)+\log ^2(2) \log (1048576)+x \log (2) \left (-5 \log ^2(2)+\log (4)+\log (2) (-40+\log (2097152))\right )+\left (x^3 \log ^3(2)-x \log (4) \log (16)-\log (2) \log ^2(16)-x^2 \log ^2(2) \log (512)+x \log ^2(2) (8+\log (524288))\right ) \log (-x)\right )}{\left (x^3 \log ^2(2)-\log ^2(16)-x^2 \left (\log ^2(2)+\log (4) \log (16)\right )+x (-\log (2) \log (32)+\log (16) \log (64))\right ) \left (-8+x (2-4 \log (2))+x^2 \log (2)+\log (32)+(-x \log (2)+\log (16)) \log (-x)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-16*x - 16*x^2*Log[2] + (-20 + 20*x - 4*x^3)*Log[2]^2 + (16*x*Log[2] + 8*x^2*Log[2]^2)*Log[-x] - 4*
x*Log[2]^2*Log[-x]^2)/(64*x - 32*x^2 + 4*x^3 + (-80*x + 84*x^2 - 32*x^3 + 4*x^4)*Log[2] + (25*x - 40*x^2 + 26*
x^3 - 8*x^4 + x^5)*Log[2]^2 + ((-64*x + 32*x^2 - 4*x^3)*Log[2] + (40*x - 42*x^2 + 16*x^3 - 2*x^4)*Log[2]^2)*Lo
g[-x] + (16*x - 8*x^2 + x^3)*Log[2]^2*Log[-x]^2),x]

[Out]

(-4*(-(x^4*Log[2]^3) + x^3*Log[2]*(5*Log[2]^2 - Log[4] + Log[2]*Log[16]) + x^2*(-15*Log[2]^3 - Log[2]^2*(-2 +
Log[16]) + Log[16]^2) - Log[2]*Log[16]*Log[32] + Log[16]*Log[256] + Log[2]^2*Log[1048576] + x*Log[2]*(-5*Log[2
]^2 + Log[4] + Log[2]*(-40 + Log[2097152])) + (x^3*Log[2]^3 - x*Log[4]*Log[16] - Log[2]*Log[16]^2 - x^2*Log[2]
^2*Log[512] + x*Log[2]^2*(8 + Log[524288]))*Log[-x]))/((x^3*Log[2]^2 - Log[16]^2 - x^2*(Log[2]^2 + Log[4]*Log[
16]) + x*(-(Log[2]*Log[32]) + Log[16]*Log[64]))*(-8 + x*(2 - 4*Log[2]) + x^2*Log[2] + Log[32] + (-(x*Log[2]) +
Log[16])*Log[-x]))

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fricas [A]  time = 0.60, size = 45, normalized size = 1.80 \begin {gather*} -\frac {4 \, {\left (x \log \relax (2) - \log \relax (2) \log \left (-x\right ) + 2\right )}}{{\left (x - 4\right )} \log \relax (2) \log \left (-x\right ) - {\left (x^{2} - 4 \, x + 5\right )} \log \relax (2) - 2 \, x + 8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x*log(2)^2*log(-x)^2+(8*x^2*log(2)^2+16*x*log(2))*log(-x)+(-4*x^3+20*x-20)*log(2)^2-16*x^2*log(2
)-16*x)/((x^3-8*x^2+16*x)*log(2)^2*log(-x)^2+((-2*x^4+16*x^3-42*x^2+40*x)*log(2)^2+(-4*x^3+32*x^2-64*x)*log(2)
)*log(-x)+(x^5-8*x^4+26*x^3-40*x^2+25*x)*log(2)^2+(4*x^4-32*x^3+84*x^2-80*x)*log(2)+4*x^3-32*x^2+64*x),x, algo
rithm="fricas")

[Out]

-4*(x*log(2) - log(2)*log(-x) + 2)/((x - 4)*log(2)*log(-x) - (x^2 - 4*x + 5)*log(2) - 2*x + 8)

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giac [B]  time = 0.20, size = 74, normalized size = 2.96 \begin {gather*} -\frac {20 \, \log \relax (2)}{x^{3} \log \relax (2) - x^{2} \log \relax (2) \log \left (-x\right ) - 8 \, x^{2} \log \relax (2) + 8 \, x \log \relax (2) \log \left (-x\right ) + 2 \, x^{2} + 21 \, x \log \relax (2) - 16 \, \log \relax (2) \log \left (-x\right ) - 16 \, x - 20 \, \log \relax (2) + 32} + \frac {4}{x - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x*log(2)^2*log(-x)^2+(8*x^2*log(2)^2+16*x*log(2))*log(-x)+(-4*x^3+20*x-20)*log(2)^2-16*x^2*log(2
)-16*x)/((x^3-8*x^2+16*x)*log(2)^2*log(-x)^2+((-2*x^4+16*x^3-42*x^2+40*x)*log(2)^2+(-4*x^3+32*x^2-64*x)*log(2)
)*log(-x)+(x^5-8*x^4+26*x^3-40*x^2+25*x)*log(2)^2+(4*x^4-32*x^3+84*x^2-80*x)*log(2)+4*x^3-32*x^2+64*x),x, algo
rithm="giac")

[Out]

-20*log(2)/(x^3*log(2) - x^2*log(2)*log(-x) - 8*x^2*log(2) + 8*x*log(2)*log(-x) + 2*x^2 + 21*x*log(2) - 16*log
(2)*log(-x) - 16*x - 20*log(2) + 32) + 4/(x - 4)

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maple [B]  time = 0.36, size = 56, normalized size = 2.24

method	result	size
norman	\(\frac {4 x \ln \relax (2)-4 \ln \relax (2) \ln \left (-x \right )+8}{x^{2} \ln \relax (2)-\ln \left (-x \right ) \ln \relax (2) x -4 x \ln \relax (2)+4 \ln \relax (2) \ln \left (-x \right )+5 \ln \relax (2)+2 x -8}\)	\(56\)
risch	\(\frac {4}{x -4}-\frac {20 \ln \relax (2)}{\left (x -4\right ) \left (x^{2} \ln \relax (2)-\ln \left (-x \right ) \ln \relax (2) x -4 x \ln \relax (2)+4 \ln \relax (2) \ln \left (-x \right )+5 \ln \relax (2)+2 x -8\right )}\)	\(57\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*x*ln(2)^2*ln(-x)^2+(8*x^2*ln(2)^2+16*x*ln(2))*ln(-x)+(-4*x^3+20*x-20)*ln(2)^2-16*x^2*ln(2)-16*x)/((x^3
-8*x^2+16*x)*ln(2)^2*ln(-x)^2+((-2*x^4+16*x^3-42*x^2+40*x)*ln(2)^2+(-4*x^3+32*x^2-64*x)*ln(2))*ln(-x)+(x^5-8*x
^4+26*x^3-40*x^2+25*x)*ln(2)^2+(4*x^4-32*x^3+84*x^2-80*x)*ln(2)+4*x^3-32*x^2+64*x),x,method=_RETURNVERBOSE)

[Out]

(4*x*ln(2)-4*ln(2)*ln(-x)+8)/(x^2*ln(2)-ln(-x)*ln(2)*x-4*x*ln(2)+4*ln(2)*ln(-x)+5*ln(2)+2*x-8)

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maxima [B]  time = 0.49, size = 54, normalized size = 2.16 \begin {gather*} \frac {4 \, {\left (x \log \relax (2) - \log \relax (2) \log \left (-x\right ) + 2\right )}}{x^{2} \log \relax (2) - 2 \, x {\left (2 \, \log \relax (2) - 1\right )} - {\left (x \log \relax (2) - 4 \, \log \relax (2)\right )} \log \left (-x\right ) + 5 \, \log \relax (2) - 8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x*log(2)^2*log(-x)^2+(8*x^2*log(2)^2+16*x*log(2))*log(-x)+(-4*x^3+20*x-20)*log(2)^2-16*x^2*log(2
)-16*x)/((x^3-8*x^2+16*x)*log(2)^2*log(-x)^2+((-2*x^4+16*x^3-42*x^2+40*x)*log(2)^2+(-4*x^3+32*x^2-64*x)*log(2)
)*log(-x)+(x^5-8*x^4+26*x^3-40*x^2+25*x)*log(2)^2+(4*x^4-32*x^3+84*x^2-80*x)*log(2)+4*x^3-32*x^2+64*x),x, algo
rithm="maxima")

[Out]

4*(x*log(2) - log(2)*log(-x) + 2)/(x^2*log(2) - 2*x*(2*log(2) - 1) - (x*log(2) - 4*log(2))*log(-x) + 5*log(2)
- 8)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {16\,x-\ln \left (-x\right )\,\left (8\,{\ln \relax (2)}^2\,x^2+16\,\ln \relax (2)\,x\right )+{\ln \relax (2)}^2\,\left (4\,x^3-20\,x+20\right )+16\,x^2\,\ln \relax (2)+4\,x\,{\ln \left (-x\right )}^2\,{\ln \relax (2)}^2}{64\,x+\ln \left (-x\right )\,\left ({\ln \relax (2)}^2\,\left (-2\,x^4+16\,x^3-42\,x^2+40\,x\right )-\ln \relax (2)\,\left (4\,x^3-32\,x^2+64\,x\right )\right )-\ln \relax (2)\,\left (-4\,x^4+32\,x^3-84\,x^2+80\,x\right )-32\,x^2+4\,x^3+{\ln \relax (2)}^2\,\left (x^5-8\,x^4+26\,x^3-40\,x^2+25\,x\right )+{\ln \left (-x\right )}^2\,{\ln \relax (2)}^2\,\left (x^3-8\,x^2+16\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(16*x - log(-x)*(8*x^2*log(2)^2 + 16*x*log(2)) + log(2)^2*(4*x^3 - 20*x + 20) + 16*x^2*log(2) + 4*x*log(-
x)^2*log(2)^2)/(64*x + log(-x)*(log(2)^2*(40*x - 42*x^2 + 16*x^3 - 2*x^4) - log(2)*(64*x - 32*x^2 + 4*x^3)) -
log(2)*(80*x - 84*x^2 + 32*x^3 - 4*x^4) - 32*x^2 + 4*x^3 + log(2)^2*(25*x - 40*x^2 + 26*x^3 - 8*x^4 + x^5) + l
og(-x)^2*log(2)^2*(16*x - 8*x^2 + x^3)),x)

[Out]

int(-(16*x - log(-x)*(8*x^2*log(2)^2 + 16*x*log(2)) + log(2)^2*(4*x^3 - 20*x + 20) + 16*x^2*log(2) + 4*x*log(-
x)^2*log(2)^2)/(64*x + log(-x)*(log(2)^2*(40*x - 42*x^2 + 16*x^3 - 2*x^4) - log(2)*(64*x - 32*x^2 + 4*x^3)) -
log(2)*(80*x - 84*x^2 + 32*x^3 - 4*x^4) - 32*x^2 + 4*x^3 + log(2)^2*(25*x - 40*x^2 + 26*x^3 - 8*x^4 + x^5) + l
og(-x)^2*log(2)^2*(16*x - 8*x^2 + x^3)), x)

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sympy [B]  time = 0.40, size = 70, normalized size = 2.80 \begin {gather*} \frac {20 \log {\relax (2 )}}{- x^{3} \log {\relax (2 )} - 2 x^{2} + 8 x^{2} \log {\relax (2 )} - 21 x \log {\relax (2 )} + 16 x + \left (x^{2} \log {\relax (2 )} - 8 x \log {\relax (2 )} + 16 \log {\relax (2 )}\right ) \log {\left (- x \right )} - 32 + 20 \log {\relax (2 )}} + \frac {4}{x - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x*ln(2)**2*ln(-x)**2+(8*x**2*ln(2)**2+16*x*ln(2))*ln(-x)+(-4*x**3+20*x-20)*ln(2)**2-16*x**2*ln(2
)-16*x)/((x**3-8*x**2+16*x)*ln(2)**2*ln(-x)**2+((-2*x**4+16*x**3-42*x**2+40*x)*ln(2)**2+(-4*x**3+32*x**2-64*x)
*ln(2))*ln(-x)+(x**5-8*x**4+26*x**3-40*x**2+25*x)*ln(2)**2+(4*x**4-32*x**3+84*x**2-80*x)*ln(2)+4*x**3-32*x**2+
64*x),x)

[Out]

20*log(2)/(-x**3*log(2) - 2*x**2 + 8*x**2*log(2) - 21*x*log(2) + 16*x + (x**2*log(2) - 8*x*log(2) + 16*log(2))
*log(-x) - 32 + 20*log(2)) + 4/(x - 4)

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