Optimal. Leaf size=23 \[ \frac {100 \log ^2(x)}{(1-x) \left (\log (x)+\log ^2(\log (4))\right )} \]
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Rubi [F] time = 1.43, 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 {(100-100 x) \log ^2(x)+100 x \log ^3(x)+\left ((200-200 x) \log (x)+100 x \log ^2(x)\right ) \log ^2(\log (4))}{\left (x-2 x^2+x^3\right ) \log ^2(x)+\left (2 x-4 x^2+2 x^3\right ) \log (x) \log ^2(\log (4))+\left (x-2 x^2+x^3\right ) \log ^4(\log (4))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {100 \log (x) \left (\log (x)+x \log ^2(x)-2 (-1+x) \log ^2(\log (4))+x \log (x) \left (-1+\log ^2(\log (4))\right )\right )}{(1-x)^2 x \left (\log (x)+\log ^2(\log (4))\right )^2} \, dx\\ &=100 \int \frac {\log (x) \left (\log (x)+x \log ^2(x)-2 (-1+x) \log ^2(\log (4))+x \log (x) \left (-1+\log ^2(\log (4))\right )\right )}{(1-x)^2 x \left (\log (x)+\log ^2(\log (4))\right )^2} \, dx\\ &=100 \int \left (\frac {\log (x)}{(-1+x)^2}+\frac {\log ^4(\log (4))}{(-1+x) x \left (\log (x)+\log ^2(\log (4))\right )^2}+\frac {\log ^4(\log (4))}{(-1+x)^2 \left (\log (x)+\log ^2(\log (4))\right )}+\frac {1-x \left (1+\log ^2(\log (4))\right )}{(1-x)^2 x}\right ) \, dx\\ &=100 \int \frac {\log (x)}{(-1+x)^2} \, dx+100 \int \frac {1-x \left (1+\log ^2(\log (4))\right )}{(1-x)^2 x} \, dx+\left (100 \log ^4(\log (4))\right ) \int \frac {1}{(-1+x) x \left (\log (x)+\log ^2(\log (4))\right )^2} \, dx+\left (100 \log ^4(\log (4))\right ) \int \frac {1}{(-1+x)^2 \left (\log (x)+\log ^2(\log (4))\right )} \, dx\\ &=\frac {100 x \log (x)}{1-x}+100 \int \frac {1}{-1+x} \, dx+100 \int \left (\frac {1}{1-x}+\frac {1}{x}-\frac {\log ^2(\log (4))}{(-1+x)^2}\right ) \, dx+\left (100 \log ^4(\log (4))\right ) \int \frac {1}{(-1+x) x \left (\log (x)+\log ^2(\log (4))\right )^2} \, dx+\left (100 \log ^4(\log (4))\right ) \int \frac {1}{(-1+x)^2 \left (\log (x)+\log ^2(\log (4))\right )} \, dx\\ &=100 \log (x)+\frac {100 x \log (x)}{1-x}-\frac {100 \log ^2(\log (4))}{1-x}+\left (100 \log ^4(\log (4))\right ) \int \frac {1}{(-1+x) x \left (\log (x)+\log ^2(\log (4))\right )^2} \, dx+\left (100 \log ^4(\log (4))\right ) \int \frac {1}{(-1+x)^2 \left (\log (x)+\log ^2(\log (4))\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.21, size = 21, normalized size = 0.91 \begin {gather*} -\frac {100 \log ^2(x)}{(-1+x) \left (\log (x)+\log ^2(\log (4))\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 26, normalized size = 1.13 \begin {gather*} -\frac {100 \, \log \relax (x)^{2}}{{\left (x - 1\right )} \log \left (2 \, \log \relax (2)\right )^{2} + {\left (x - 1\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.28, size = 127, normalized size = 5.52 \begin {gather*} -\frac {100 \, {\left (\log \relax (2)^{4} + 4 \, \log \relax (2)^{3} \log \left (\log \relax (2)\right ) + 6 \, \log \relax (2)^{2} \log \left (\log \relax (2)\right )^{2} + 4 \, \log \relax (2) \log \left (\log \relax (2)\right )^{3} + \log \left (\log \relax (2)\right )^{4}\right )}}{x \log \relax (2)^{2} + 2 \, x \log \relax (2) \log \left (\log \relax (2)\right ) + x \log \left (\log \relax (2)\right )^{2} - \log \relax (2)^{2} + x \log \relax (x) - 2 \, \log \relax (2) \log \left (\log \relax (2)\right ) - \log \left (\log \relax (2)\right )^{2} - \log \relax (x)} + \frac {100 \, {\left (\log \relax (2)^{2} + 2 \, \log \relax (2) \log \left (\log \relax (2)\right ) + \log \left (\log \relax (2)\right )^{2}\right )}}{x - 1} - \frac {100 \, \log \relax (x)}{x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.42, size = 24, normalized size = 1.04
method | result | size |
norman | \(-\frac {100 \ln \relax (x )^{2}}{\left (x -1\right ) \left (\ln \relax (x )+\ln \left (2 \ln \relax (2)\right )^{2}\right )}\) | \(24\) |
risch | \(-\frac {100 \ln \relax (x )}{x -1}+\frac {100 \ln \relax (2)^{2}}{x -1}+\frac {200 \ln \relax (2) \ln \left (\ln \relax (2)\right )}{x -1}+\frac {100 \ln \left (\ln \relax (2)\right )^{2}}{x -1}-\frac {100 \left (\ln \relax (2)^{4}+4 \ln \relax (2)^{3} \ln \left (\ln \relax (2)\right )+6 \ln \relax (2)^{2} \ln \left (\ln \relax (2)\right )^{2}+4 \ln \relax (2) \ln \left (\ln \relax (2)\right )^{3}+\ln \left (\ln \relax (2)\right )^{4}\right )}{\left (x -1\right ) \left (\ln \relax (2)^{2}+2 \ln \relax (2) \ln \left (\ln \relax (2)\right )+\ln \left (\ln \relax (2)\right )^{2}+\ln \relax (x )\right )}\) | \(113\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.50, size = 54, normalized size = 2.35 \begin {gather*} -\frac {100 \, \log \relax (x)^{2}}{{\left (\log \relax (2)^{2} + 2 \, \log \relax (2) \log \left (\log \relax (2)\right ) + \log \left (\log \relax (2)\right )^{2}\right )} x - \log \relax (2)^{2} + {\left (x - 1\right )} \log \relax (x) - 2 \, \log \relax (2) \log \left (\log \relax (2)\right ) - \log \left (\log \relax (2)\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.84, size = 21, normalized size = 0.91 \begin {gather*} -\frac {100\,{\ln \relax (x)}^2}{\left (\ln \relax (x)+{\ln \left (\ln \relax (4)\right )}^2\right )\,\left (x-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.31, size = 148, normalized size = 6.43 \begin {gather*} \frac {- 600 \log {\relax (2 )}^{2} \log {\left (\log {\relax (2 )} \right )}^{2} - 100 \log {\relax (2 )}^{4} - 100 \log {\left (\log {\relax (2 )} \right )}^{4} - 400 \log {\relax (2 )} \log {\left (\log {\relax (2 )} \right )}^{3} - 400 \log {\relax (2 )}^{3} \log {\left (\log {\relax (2 )} \right )}}{2 x \log {\relax (2 )} \log {\left (\log {\relax (2 )} \right )} + x \log {\left (\log {\relax (2 )} \right )}^{2} + x \log {\relax (2 )}^{2} + \left (x - 1\right ) \log {\relax (x )} - \log {\relax (2 )}^{2} - \log {\left (\log {\relax (2 )} \right )}^{2} - 2 \log {\relax (2 )} \log {\left (\log {\relax (2 )} \right )}} - \frac {100 \log {\relax (x )}}{x - 1} - \frac {- 100 \log {\relax (2 )}^{2} - 100 \log {\left (\log {\relax (2 )} \right )}^{2} - 200 \log {\relax (2 )} \log {\left (\log {\relax (2 )} \right )}}{x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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