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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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