Optimal. Leaf size=24 \[ \log (x)+(-1+x)^2 \log ^4\left (1-\left (-4+\log \left (x^2\right )\right )^2\right ) \]
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Rubi [F] time = 8.38, 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 {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{x}+\frac {16 (-1+x)^2 \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{x \left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )}+2 (-1+x) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )\right ) \, dx\\ &=\log (x)+2 \int (-1+x) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+16 \int \frac {(-1+x)^2 \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{x \left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )} \, dx\\ &=\log (x)+2 \int \left (-\log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+x \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )\right ) \, dx+16 \int \left (-\frac {2 \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{\left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )}+\frac {\left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{x \left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )}+\frac {x \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{\left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )}\right ) \, dx\\ &=\log (x)-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+2 \int x \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+16 \int \frac {\left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{x \left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )} \, dx+16 \int \frac {x \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{\left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )} \, dx-32 \int \frac {\left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{\left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )} \, dx\\ &=\log (x)-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \operatorname {Subst}\left (\int \frac {(-4+x) \log ^3\left (-15+8 x-x^2\right )}{(-5+x) (-3+x)} \, dx,x,\log \left (x^2\right )\right )+8 \operatorname {Subst}\left (\int \frac {(-4+\log (x)) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{(-5+\log (x)) (-3+\log (x))} \, dx,x,x^2\right )-32 \int \left (-\frac {4 \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )}+\frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )}\right ) \, dx+\operatorname {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right )\\ &=\log (x)-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \operatorname {Subst}\left (\int \left (\frac {\log ^3\left (-15+8 x-x^2\right )}{2 (-5+x)}+\frac {\log ^3\left (-15+8 x-x^2\right )}{2 (-3+x)}\right ) \, dx,x,\log \left (x^2\right )\right )+8 \operatorname {Subst}\left (\int \left (-\frac {4 \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)}+\frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)}\right ) \, dx,x,x^2\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\operatorname {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right )\\ &=\log (x)-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+4 \operatorname {Subst}\left (\int \frac {\log ^3\left (-15+8 x-x^2\right )}{-5+x} \, dx,x,\log \left (x^2\right )\right )+4 \operatorname {Subst}\left (\int \frac {\log ^3\left (-15+8 x-x^2\right )}{-3+x} \, dx,x,\log \left (x^2\right )\right )+8 \operatorname {Subst}\left (\int \frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-32 \operatorname {Subst}\left (\int \frac {\log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\operatorname {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right )\\ &=\log (x)+4 \log \left (-5+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+4 \log \left (-3+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \operatorname {Subst}\left (\int \frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )-12 \operatorname {Subst}\left (\int \frac {(8-2 x) \log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-15+8 x-x^2} \, dx,x,\log \left (x^2\right )\right )-12 \operatorname {Subst}\left (\int \frac {(8-2 x) \log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-15+8 x-x^2} \, dx,x,\log \left (x^2\right )\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-32 \operatorname {Subst}\left (\int \frac {\log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\operatorname {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right )\\ &=\log (x)+4 \log \left (-5+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+4 \log \left (-3+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \operatorname {Subst}\left (\int \frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )-12 \operatorname {Subst}\left (\int \left (\frac {\log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-5+x}+\frac {\log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-3+x}\right ) \, dx,x,\log \left (x^2\right )\right )-12 \operatorname {Subst}\left (\int \left (\frac {\log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-5+x}+\frac {\log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-3+x}\right ) \, dx,x,\log \left (x^2\right )\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-32 \operatorname {Subst}\left (\int \frac {\log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\operatorname {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right )\\ &=\log (x)+4 \log \left (-5+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+4 \log \left (-3+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \operatorname {Subst}\left (\int \frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )-12 \operatorname {Subst}\left (\int \frac {\log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-5+x} \, dx,x,\log \left (x^2\right )\right )-12 \operatorname {Subst}\left (\int \frac {\log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-3+x} \, dx,x,\log \left (x^2\right )\right )-12 \operatorname {Subst}\left (\int \frac {\log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-5+x} \, dx,x,\log \left (x^2\right )\right )-12 \operatorname {Subst}\left (\int \frac {\log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-3+x} \, dx,x,\log \left (x^2\right )\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-32 \operatorname {Subst}\left (\int \frac {\log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\operatorname {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 28, normalized size = 1.17 \begin {gather*} \log (x)+(-1+x)^2 \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 35, normalized size = 1.46 \begin {gather*} {\left (x^{2} - 2 \, x + 1\right )} \log \left (-\log \left (x^{2}\right )^{2} + 8 \, \log \left (x^{2}\right ) - 15\right )^{4} + \frac {1}{2} \, \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 3.65, size = 31, normalized size = 1.29 \begin {gather*} {\left (x^{2} - 2 \, x + 1\right )} \log \left (-\log \left (x^{2}\right )^{2} + 8 \, \log \left (x^{2}\right ) - 15\right )^{4} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (2 x^{2}-2 x \right ) \ln \left (x^{2}\right )^{2}+\left (-16 x^{2}+16 x \right ) \ln \left (x^{2}\right )+30 x^{2}-30 x \right ) \ln \left (-\ln \left (x^{2}\right )^{2}+8 \ln \left (x^{2}\right )-15\right )^{4}+\left (\left (16 x^{2}-32 x +16\right ) \ln \left (x^{2}\right )-64 x^{2}+128 x -64\right ) \ln \left (-\ln \left (x^{2}\right )^{2}+8 \ln \left (x^{2}\right )-15\right )^{3}+\ln \left (x^{2}\right )^{2}-8 \ln \left (x^{2}\right )+15}{x \ln \left (x^{2}\right )^{2}-8 x \ln \left (x^{2}\right )+15 x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.70, size = 284, normalized size = 11.83 \begin {gather*} {\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, \log \relax (x) - 3\right )^{4} + 4 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, \log \relax (x) - 3\right )^{3} \log \left (-2 \, \log \relax (x) + 5\right ) + 6 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, \log \relax (x) - 3\right )^{2} \log \left (-2 \, \log \relax (x) + 5\right )^{2} + 4 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, \log \relax (x) - 3\right ) \log \left (-2 \, \log \relax (x) + 5\right )^{3} + {\left (x^{2} - 2 \, x + 1\right )} \log \left (-2 \, \log \relax (x) + 5\right )^{4} - \frac {1}{4} \, {\left (\log \left (\log \relax (x) - \frac {3}{2}\right ) - \log \left (\log \relax (x) - \frac {5}{2}\right )\right )} \log \left (x^{2}\right )^{2} + \frac {1}{2} \, {\left ({\left (2 \, \log \relax (x) - 3\right )} \log \left (\log \relax (x) - \frac {3}{2}\right ) - {\left (2 \, \log \relax (x) - 5\right )} \log \left (\log \relax (x) - \frac {5}{2}\right ) - 2\right )} \log \left (x^{2}\right ) + 2 \, {\left (\log \left (\log \relax (x) - \frac {3}{2}\right ) - \log \left (\log \relax (x) - \frac {5}{2}\right )\right )} \log \left (x^{2}\right ) - {\left (\log \relax (x)^{2} - 3 \, \log \relax (x)\right )} \log \left (\log \relax (x) - \frac {3}{2}\right ) - 2 \, {\left (2 \, \log \relax (x) - 3\right )} \log \left (\log \relax (x) - \frac {3}{2}\right ) + {\left (\log \relax (x)^{2} - 5 \, \log \relax (x)\right )} \log \left (\log \relax (x) - \frac {5}{2}\right ) + 2 \, {\left (2 \, \log \relax (x) - 5\right )} \log \left (\log \relax (x) - \frac {5}{2}\right ) + 3 \, \log \relax (x) - \frac {9}{4} \, \log \left (2 \, \log \relax (x) - 3\right ) + \frac {25}{4} \, \log \left (2 \, \log \relax (x) - 5\right ) - \frac {15}{4} \, \log \left (\log \relax (x) - \frac {3}{2}\right ) + \frac {15}{4} \, \log \left (\log \relax (x) - \frac {5}{2}\right ) + 4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.87, size = 29, normalized size = 1.21 \begin {gather*} \left (x^2-2\,x+1\right )\,{\ln \left (\ln \left (x^{16}\right )-{\ln \left (x^2\right )}^2-15\right )}^4+\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.47, size = 29, normalized size = 1.21 \begin {gather*} \left (x^{2} - 2 x + 1\right ) \log {\left (- \log {\left (x^{2} \right )}^{2} + 8 \log {\left (x^{2} \right )} - 15 \right )}^{4} + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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