3.4.85 \(\int \frac {8 x+25600 \log (\frac {1}{x})+2560 \log ^2(\frac {1}{x})+(-5120 \log (\frac {1}{x})-256 \log ^2(\frac {1}{x})) \log (x)+256 \log (\frac {1}{x}) \log ^2(x)+(-40+8 x-12800 \log ^2(\frac {1}{x})+2560 \log ^2(\frac {1}{x}) \log (x)-128 \log ^2(\frac {1}{x}) \log ^2(x)) \log (5-x+1600 \log ^2(\frac {1}{x})-320 \log ^2(\frac {1}{x}) \log (x)+16 \log ^2(\frac {1}{x}) \log ^2(x))}{(5 x^3-x^4+1600 x^3 \log ^2(\frac {1}{x})-320 x^3 \log ^2(\frac {1}{x}) \log (x)+16 x^3 \log ^2(\frac {1}{x}) \log ^2(x)) \log ^3(5-x+1600 \log ^2(\frac {1}{x})-320 \log ^2(\frac {1}{x}) \log (x)+16 \log ^2(\frac {1}{x}) \log ^2(x))} \, dx\)

Optimal. Leaf size=27 \[ \frac {4}{x^2 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \]

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Rubi [F]  time = 10.56, 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 {8 x+25600 \log \left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right )+\left (-5120 \log \left (\frac {1}{x}\right )-256 \log ^2\left (\frac {1}{x}\right )\right ) \log (x)+256 \log \left (\frac {1}{x}\right ) \log ^2(x)+\left (-40+8 x-12800 \log ^2\left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right ) \log (x)-128 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log \left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )}{\left (5 x^3-x^4+1600 x^3 \log ^2\left (\frac {1}{x}\right )-320 x^3 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 x^3 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(8*x + 25600*Log[x^(-1)] + 2560*Log[x^(-1)]^2 + (-5120*Log[x^(-1)] - 256*Log[x^(-1)]^2)*Log[x] + 256*Log[x
^(-1)]*Log[x]^2 + (-40 + 8*x - 12800*Log[x^(-1)]^2 + 2560*Log[x^(-1)]^2*Log[x] - 128*Log[x^(-1)]^2*Log[x]^2)*L
og[5 - x + 1600*Log[x^(-1)]^2 - 320*Log[x^(-1)]^2*Log[x] + 16*Log[x^(-1)]^2*Log[x]^2])/((5*x^3 - x^4 + 1600*x^
3*Log[x^(-1)]^2 - 320*x^3*Log[x^(-1)]^2*Log[x] + 16*x^3*Log[x^(-1)]^2*Log[x]^2)*Log[5 - x + 1600*Log[x^(-1)]^2
- 320*Log[x^(-1)]^2*Log[x] + 16*Log[x^(-1)]^2*Log[x]^2]^3),x]

[Out]

-8*Defer[Int][1/(x^2*(-5 + x - 16*Log[x^(-1)]^2*(-10 + Log[x])^2)*Log[5 - x + 16*Log[x^(-1)]^2*(-10 + Log[x])^
2]^3), x] - 25600*Defer[Int][Log[x^(-1)]/(x^3*(-5 + x - 16*Log[x^(-1)]^2*(-10 + Log[x])^2)*Log[5 - x + 16*Log[
x^(-1)]^2*(-10 + Log[x])^2]^3), x] - 2560*Defer[Int][Log[x^(-1)]^2/(x^3*(-5 + x - 16*Log[x^(-1)]^2*(-10 + Log[
x])^2)*Log[5 - x + 16*Log[x^(-1)]^2*(-10 + Log[x])^2]^3), x] + 5120*Defer[Int][(Log[x^(-1)]*Log[x])/(x^3*(-5 +
x - 16*Log[x^(-1)]^2*(-10 + Log[x])^2)*Log[5 - x + 16*Log[x^(-1)]^2*(-10 + Log[x])^2]^3), x] + 256*Defer[Int]
[(Log[x^(-1)]^2*Log[x])/(x^3*(-5 + x - 16*Log[x^(-1)]^2*(-10 + Log[x])^2)*Log[5 - x + 16*Log[x^(-1)]^2*(-10 +
Log[x])^2]^3), x] - 256*Defer[Int][(Log[x^(-1)]*Log[x]^2)/(x^3*(-5 + x - 16*Log[x^(-1)]^2*(-10 + Log[x])^2)*Lo
g[5 - x + 16*Log[x^(-1)]^2*(-10 + Log[x])^2]^3), x] - 8*Defer[Int][1/(x^3*Log[5 - x + 16*Log[x^(-1)]^2*(-10 +
Log[x])^2]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 \left (x+32 \log \left (\frac {1}{x}\right ) (-10+\log (x))^2+(-5+x) \log \left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )-16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x)) \left (2+(-10+\log (x)) \log \left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )\right )\right )}{x^3 \left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx\\ &=8 \int \frac {x+32 \log \left (\frac {1}{x}\right ) (-10+\log (x))^2+(-5+x) \log \left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )-16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x)) \left (2+(-10+\log (x)) \log \left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )\right )}{x^3 \left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx\\ &=8 \int \left (\frac {-x-3200 \log \left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right )+640 \log \left (\frac {1}{x}\right ) \log (x)+32 \log ^2\left (\frac {1}{x}\right ) \log (x)-32 \log \left (\frac {1}{x}\right ) \log ^2(x)}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )}-\frac {1}{x^3 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )}\right ) \, dx\\ &=8 \int \frac {-x-3200 \log \left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right )+640 \log \left (\frac {1}{x}\right ) \log (x)+32 \log ^2\left (\frac {1}{x}\right ) \log (x)-32 \log \left (\frac {1}{x}\right ) \log ^2(x)}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx-8 \int \frac {1}{x^3 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx\\ &=8 \int \frac {x-32 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))+32 \log \left (\frac {1}{x}\right ) (-10+\log (x))^2}{x^3 \left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx-8 \int \frac {1}{x^3 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx\\ &=8 \int \left (-\frac {1}{x^2 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )}-\frac {3200 \log \left (\frac {1}{x}\right )}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )}-\frac {320 \log ^2\left (\frac {1}{x}\right )}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )}+\frac {640 \log \left (\frac {1}{x}\right ) \log (x)}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )}+\frac {32 \log ^2\left (\frac {1}{x}\right ) \log (x)}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )}-\frac {32 \log \left (\frac {1}{x}\right ) \log ^2(x)}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )}\right ) \, dx-8 \int \frac {1}{x^3 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx\\ &=-\left (8 \int \frac {1}{x^2 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx\right )-8 \int \frac {1}{x^3 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx+256 \int \frac {\log ^2\left (\frac {1}{x}\right ) \log (x)}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx-256 \int \frac {\log \left (\frac {1}{x}\right ) \log ^2(x)}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx-2560 \int \frac {\log ^2\left (\frac {1}{x}\right )}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx+5120 \int \frac {\log \left (\frac {1}{x}\right ) \log (x)}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx-25600 \int \frac {\log \left (\frac {1}{x}\right )}{x^3 \left (-5+x-1600 \log ^2\left (\frac {1}{x}\right )+320 \log ^2\left (\frac {1}{x}\right ) \log (x)-16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx\\ &=-\left (8 \int \frac {1}{x^2 \left (-5+x-16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx\right )-8 \int \frac {1}{x^3 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx+256 \int \frac {\log ^2\left (\frac {1}{x}\right ) \log (x)}{x^3 \left (-5+x-16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx-256 \int \frac {\log \left (\frac {1}{x}\right ) \log ^2(x)}{x^3 \left (-5+x-16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx-2560 \int \frac {\log ^2\left (\frac {1}{x}\right )}{x^3 \left (-5+x-16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx+5120 \int \frac {\log \left (\frac {1}{x}\right ) \log (x)}{x^3 \left (-5+x-16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx-25600 \int \frac {\log \left (\frac {1}{x}\right )}{x^3 \left (-5+x-16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right ) \log ^3\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 27, normalized size = 1.00 \begin {gather*} \frac {4}{x^2 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(8*x + 25600*Log[x^(-1)] + 2560*Log[x^(-1)]^2 + (-5120*Log[x^(-1)] - 256*Log[x^(-1)]^2)*Log[x] + 256
*Log[x^(-1)]*Log[x]^2 + (-40 + 8*x - 12800*Log[x^(-1)]^2 + 2560*Log[x^(-1)]^2*Log[x] - 128*Log[x^(-1)]^2*Log[x
]^2)*Log[5 - x + 1600*Log[x^(-1)]^2 - 320*Log[x^(-1)]^2*Log[x] + 16*Log[x^(-1)]^2*Log[x]^2])/((5*x^3 - x^4 + 1
600*x^3*Log[x^(-1)]^2 - 320*x^3*Log[x^(-1)]^2*Log[x] + 16*x^3*Log[x^(-1)]^2*Log[x]^2)*Log[5 - x + 1600*Log[x^(
-1)]^2 - 320*Log[x^(-1)]^2*Log[x] + 16*Log[x^(-1)]^2*Log[x]^2]^3),x]

[Out]

4/(x^2*Log[5 - x + 16*Log[x^(-1)]^2*(-10 + Log[x])^2]^2)

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fricas [A]  time = 0.65, size = 37, normalized size = 1.37 \begin {gather*} \frac {4}{x^{2} \log \left (16 \, \log \left (\frac {1}{x}\right )^{4} + 320 \, \log \left (\frac {1}{x}\right )^{3} + 1600 \, \log \left (\frac {1}{x}\right )^{2} - x + 5\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-128*log(1/x)^2*log(x)^2+2560*log(1/x)^2*log(x)-12800*log(1/x)^2+8*x-40)*log(16*log(1/x)^2*log(x)^
2-320*log(1/x)^2*log(x)+1600*log(1/x)^2+5-x)+256*log(1/x)*log(x)^2+(-256*log(1/x)^2-5120*log(1/x))*log(x)+2560
*log(1/x)^2+25600*log(1/x)+8*x)/(16*x^3*log(1/x)^2*log(x)^2-320*x^3*log(1/x)^2*log(x)+1600*x^3*log(1/x)^2-x^4+
5*x^3)/log(16*log(1/x)^2*log(x)^2-320*log(1/x)^2*log(x)+1600*log(1/x)^2+5-x)^3,x, algorithm="fricas")

[Out]

4/(x^2*log(16*log(1/x)^4 + 320*log(1/x)^3 + 1600*log(1/x)^2 - x + 5)^2)

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giac [B]  time = 2.06, size = 159, normalized size = 5.89 \begin {gather*} \frac {4 \, {\left (64 \, \log \relax (x)^{3} - 960 \, \log \relax (x)^{2} - x + 3200 \, \log \relax (x)\right )}}{64 \, x^{2} \log \left (16 \, \log \relax (x)^{4} - 320 \, \log \relax (x)^{3} + 1600 \, \log \relax (x)^{2} - x + 5\right )^{2} \log \relax (x)^{3} - 960 \, x^{2} \log \left (16 \, \log \relax (x)^{4} - 320 \, \log \relax (x)^{3} + 1600 \, \log \relax (x)^{2} - x + 5\right )^{2} \log \relax (x)^{2} - x^{3} \log \left (16 \, \log \relax (x)^{4} - 320 \, \log \relax (x)^{3} + 1600 \, \log \relax (x)^{2} - x + 5\right )^{2} + 3200 \, x^{2} \log \left (16 \, \log \relax (x)^{4} - 320 \, \log \relax (x)^{3} + 1600 \, \log \relax (x)^{2} - x + 5\right )^{2} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-128*log(1/x)^2*log(x)^2+2560*log(1/x)^2*log(x)-12800*log(1/x)^2+8*x-40)*log(16*log(1/x)^2*log(x)^
2-320*log(1/x)^2*log(x)+1600*log(1/x)^2+5-x)+256*log(1/x)*log(x)^2+(-256*log(1/x)^2-5120*log(1/x))*log(x)+2560
*log(1/x)^2+25600*log(1/x)+8*x)/(16*x^3*log(1/x)^2*log(x)^2-320*x^3*log(1/x)^2*log(x)+1600*x^3*log(1/x)^2-x^4+
5*x^3)/log(16*log(1/x)^2*log(x)^2-320*log(1/x)^2*log(x)+1600*log(1/x)^2+5-x)^3,x, algorithm="giac")

[Out]

4*(64*log(x)^3 - 960*log(x)^2 - x + 3200*log(x))/(64*x^2*log(16*log(x)^4 - 320*log(x)^3 + 1600*log(x)^2 - x +
5)^2*log(x)^3 - 960*x^2*log(16*log(x)^4 - 320*log(x)^3 + 1600*log(x)^2 - x + 5)^2*log(x)^2 - x^3*log(16*log(x)
^4 - 320*log(x)^3 + 1600*log(x)^2 - x + 5)^2 + 3200*x^2*log(16*log(x)^4 - 320*log(x)^3 + 1600*log(x)^2 - x + 5
)^2*log(x))

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maple [A]  time = 0.40, size = 32, normalized size = 1.19

method	result	size
risch	\(\frac {4}{x^{2} \ln \left (16 \ln \relax (x )^{4}-320 \ln \relax (x )^{3}+1600 \ln \relax (x )^{2}+5-x \right )^{2}}\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-128*ln(1/x)^2*ln(x)^2+2560*ln(1/x)^2*ln(x)-12800*ln(1/x)^2+8*x-40)*ln(16*ln(1/x)^2*ln(x)^2-320*ln(1/x)^
2*ln(x)+1600*ln(1/x)^2+5-x)+256*ln(1/x)*ln(x)^2+(-256*ln(1/x)^2-5120*ln(1/x))*ln(x)+2560*ln(1/x)^2+25600*ln(1/
x)+8*x)/(16*x^3*ln(1/x)^2*ln(x)^2-320*x^3*ln(1/x)^2*ln(x)+1600*x^3*ln(1/x)^2-x^4+5*x^3)/ln(16*ln(1/x)^2*ln(x)^
2-320*ln(1/x)^2*ln(x)+1600*ln(1/x)^2+5-x)^3,x,method=_RETURNVERBOSE)

[Out]

4/x^2/ln(16*ln(x)^4-320*ln(x)^3+1600*ln(x)^2+5-x)^2

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maxima [A]  time = 0.48, size = 31, normalized size = 1.15 \begin {gather*} \frac {4}{x^{2} \log \left (16 \, \log \relax (x)^{4} - 320 \, \log \relax (x)^{3} + 1600 \, \log \relax (x)^{2} - x + 5\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-128*log(1/x)^2*log(x)^2+2560*log(1/x)^2*log(x)-12800*log(1/x)^2+8*x-40)*log(16*log(1/x)^2*log(x)^
2-320*log(1/x)^2*log(x)+1600*log(1/x)^2+5-x)+256*log(1/x)*log(x)^2+(-256*log(1/x)^2-5120*log(1/x))*log(x)+2560
*log(1/x)^2+25600*log(1/x)+8*x)/(16*x^3*log(1/x)^2*log(x)^2-320*x^3*log(1/x)^2*log(x)+1600*x^3*log(1/x)^2-x^4+
5*x^3)/log(16*log(1/x)^2*log(x)^2-320*log(1/x)^2*log(x)+1600*log(1/x)^2+5-x)^3,x, algorithm="maxima")

[Out]

4/(x^2*log(16*log(x)^4 - 320*log(x)^3 + 1600*log(x)^2 - x + 5)^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {8\,x+25600\,\ln \left (\frac {1}{x}\right )-\ln \relax (x)\,\left (256\,{\ln \left (\frac {1}{x}\right )}^2+5120\,\ln \left (\frac {1}{x}\right )\right )-\ln \left (16\,{\ln \left (\frac {1}{x}\right )}^2\,{\ln \relax (x)}^2-320\,{\ln \left (\frac {1}{x}\right )}^2\,\ln \relax (x)+1600\,{\ln \left (\frac {1}{x}\right )}^2-x+5\right )\,\left (128\,{\ln \left (\frac {1}{x}\right )}^2\,{\ln \relax (x)}^2-2560\,{\ln \left (\frac {1}{x}\right )}^2\,\ln \relax (x)+12800\,{\ln \left (\frac {1}{x}\right )}^2-8\,x+40\right )+2560\,{\ln \left (\frac {1}{x}\right )}^2+256\,\ln \left (\frac {1}{x}\right )\,{\ln \relax (x)}^2}{{\ln \left (16\,{\ln \left (\frac {1}{x}\right )}^2\,{\ln \relax (x)}^2-320\,{\ln \left (\frac {1}{x}\right )}^2\,\ln \relax (x)+1600\,{\ln \left (\frac {1}{x}\right )}^2-x+5\right )}^3\,\left (-x^4+16\,x^3\,{\ln \left (\frac {1}{x}\right )}^2\,{\ln \relax (x)}^2-320\,x^3\,{\ln \left (\frac {1}{x}\right )}^2\,\ln \relax (x)+1600\,x^3\,{\ln \left (\frac {1}{x}\right )}^2+5\,x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*x + 25600*log(1/x) - log(x)*(5120*log(1/x) + 256*log(1/x)^2) - log(16*log(1/x)^2*log(x)^2 - x + 1600*lo
g(1/x)^2 - 320*log(1/x)^2*log(x) + 5)*(128*log(1/x)^2*log(x)^2 - 8*x + 12800*log(1/x)^2 - 2560*log(1/x)^2*log(
x) + 40) + 2560*log(1/x)^2 + 256*log(1/x)*log(x)^2)/(log(16*log(1/x)^2*log(x)^2 - x + 1600*log(1/x)^2 - 320*lo
g(1/x)^2*log(x) + 5)^3*(5*x^3 - x^4 + 1600*x^3*log(1/x)^2 + 16*x^3*log(1/x)^2*log(x)^2 - 320*x^3*log(1/x)^2*lo
g(x))),x)

[Out]

int((8*x + 25600*log(1/x) - log(x)*(5120*log(1/x) + 256*log(1/x)^2) - log(16*log(1/x)^2*log(x)^2 - x + 1600*lo
g(1/x)^2 - 320*log(1/x)^2*log(x) + 5)*(128*log(1/x)^2*log(x)^2 - 8*x + 12800*log(1/x)^2 - 2560*log(1/x)^2*log(
x) + 40) + 2560*log(1/x)^2 + 256*log(1/x)*log(x)^2)/(log(16*log(1/x)^2*log(x)^2 - x + 1600*log(1/x)^2 - 320*lo
g(1/x)^2*log(x) + 5)^3*(5*x^3 - x^4 + 1600*x^3*log(1/x)^2 + 16*x^3*log(1/x)^2*log(x)^2 - 320*x^3*log(1/x)^2*lo
g(x))), x)

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sympy [A]  time = 0.49, size = 31, normalized size = 1.15 \begin {gather*} \frac {4}{x^{2} \log {\left (- x + 16 \log {\relax (x )}^{4} - 320 \log {\relax (x )}^{3} + 1600 \log {\relax (x )}^{2} + 5 \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-128*ln(1/x)**2*ln(x)**2+2560*ln(1/x)**2*ln(x)-12800*ln(1/x)**2+8*x-40)*ln(16*ln(1/x)**2*ln(x)**2-
320*ln(1/x)**2*ln(x)+1600*ln(1/x)**2+5-x)+256*ln(1/x)*ln(x)**2+(-256*ln(1/x)**2-5120*ln(1/x))*ln(x)+2560*ln(1/
x)**2+25600*ln(1/x)+8*x)/(16*x**3*ln(1/x)**2*ln(x)**2-320*x**3*ln(1/x)**2*ln(x)+1600*x**3*ln(1/x)**2-x**4+5*x*
*3)/ln(16*ln(1/x)**2*ln(x)**2-320*ln(1/x)**2*ln(x)+1600*ln(1/x)**2+5-x)**3,x)

[Out]

4/(x**2*log(-x + 16*log(x)**4 - 320*log(x)**3 + 1600*log(x)**2 + 5)**2)

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