Optimal. Leaf size=26 \[ \frac {1}{5} x \left (-5+\frac {2 \left (-2 x+\log \left (\log \left (\log \left (x^2\right )\right )\right )\right )}{2-x}\right ) \]
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Rubi [F]
time = 0.75, 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 {8-4 x+\left (-20+4 x-x^2\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+4 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right )}{\left (20-20 x+5 x^2\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\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 {8-4 x+\left (-20+4 x-x^2\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+4 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right )}{5 (-2+x)^2 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx\\ &=\frac {1}{5} \int \frac {8-4 x+\left (-20+4 x-x^2\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+4 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (\log \left (\log \left (x^2\right )\right )\right )}{(-2+x)^2 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx\\ &=\frac {1}{5} \int \left (\frac {8-4 x-20 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+4 x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )-x^2 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}{(-2+x)^2 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}+\frac {4 \log \left (\log \left (\log \left (x^2\right )\right )\right )}{(-2+x)^2}\right ) \, dx\\ &=\frac {1}{5} \int \frac {8-4 x-20 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+4 x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )-x^2 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}{(-2+x)^2 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx+\frac {4}{5} \int \frac {\log \left (\log \left (\log \left (x^2\right )\right )\right )}{(-2+x)^2} \, dx\\ &=\frac {1}{5} \int \frac {8-4 x-\left (20-4 x+x^2\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}{(2-x)^2 \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx+\frac {4}{5} \int \frac {\log \left (\log \left (\log \left (x^2\right )\right )\right )}{(-2+x)^2} \, dx\\ &=\frac {1}{5} \int \left (\frac {-20+4 x-x^2}{(-2+x)^2}-\frac {4}{(-2+x) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )}\right ) \, dx+\frac {4}{5} \int \frac {\log \left (\log \left (\log \left (x^2\right )\right )\right )}{(-2+x)^2} \, dx\\ &=\frac {1}{5} \int \frac {-20+4 x-x^2}{(-2+x)^2} \, dx-\frac {4}{5} \int \frac {1}{(-2+x) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx+\frac {4}{5} \int \frac {\log \left (\log \left (\log \left (x^2\right )\right )\right )}{(-2+x)^2} \, dx\\ &=\frac {1}{5} \int \left (-1-\frac {16}{(-2+x)^2}\right ) \, dx-\frac {4}{5} \int \frac {1}{(-2+x) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx+\frac {4}{5} \int \frac {\log \left (\log \left (\log \left (x^2\right )\right )\right )}{(-2+x)^2} \, dx\\ &=-\frac {16}{5 (2-x)}-\frac {x}{5}-\frac {4}{5} \int \frac {1}{(-2+x) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )} \, dx+\frac {4}{5} \int \frac {\log \left (\log \left (\log \left (x^2\right )\right )\right )}{(-2+x)^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 26, normalized size = 1.00 \begin {gather*} -\frac {-16-2 x+x^2+2 x \log \left (\log \left (\log \left (x^2\right )\right )\right )}{5 (-2+x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 1.09, size = 0, normalized size = 0.00 \[\int \frac {4 \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right ) \ln \left (\ln \left (\ln \left (x^{2}\right )\right )\right )+\left (-x^{2}+4 x -20\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )-4 x +8}{\left (5 x^{2}-20 x +20\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 25, normalized size = 0.96 \begin {gather*} -\frac {x^{2} + 2 \, x \log \left (\log \left (2\right ) + \log \left (\log \left (x\right )\right )\right ) - 2 \, x - 16}{5 \, {\left (x - 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 24, normalized size = 0.92 \begin {gather*} -\frac {x^{2} + 2 \, x \log \left (\log \left (\log \left (x^{2}\right )\right )\right ) - 2 \, x - 16}{5 \, {\left (x - 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.27, size = 36, normalized size = 1.38 \begin {gather*} - \frac {x}{5} - \frac {2 \log {\left (\log {\left (\log {\left (x^{2} \right )} \right )} \right )}}{5} - \frac {4 \log {\left (\log {\left (\log {\left (x^{2} \right )} \right )} \right )}}{5 x - 10} + \frac {16}{5 x - 10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.49, size = 32, normalized size = 1.23 \begin {gather*} -\frac {1}{5} \, x - \frac {4 \, \log \left (\log \left (\log \left (x^{2}\right )\right )\right )}{5 \, {\left (x - 2\right )}} + \frac {16}{5 \, {\left (x - 2\right )}} - \frac {2}{5} \, \log \left (\log \left (\log \left (x^{2}\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.11, size = 46, normalized size = 1.77 \begin {gather*} \frac {16}{5\,\left (x-2\right )}-\frac {2\,\ln \left (\ln \left (\ln \left (x^2\right )\right )\right )}{5}-\frac {x}{5}+\frac {\ln \left (\ln \left (\ln \left (x^2\right )\right )\right )\,\left (8\,x-4\,x^2\right )}{5\,x\,{\left (x-2\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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