Optimal. Leaf size=18 \[ -\frac {2 \log (x)}{x \log ^2\left (\log ^2\left (4 x^2\right )\right )} \]
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Rubi [F] time = 0.64, 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 {16 \log (x)+(-2+2 \log (x)) \log \left (4 x^2\right ) \log \left (\log ^2\left (4 x^2\right )\right )}{x^2 \log \left (4 x^2\right ) \log ^3\left (\log ^2\left (4 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 \left (\frac {16 \log (x)}{x^2 \log \left (4 x^2\right ) \log ^3\left (\log ^2\left (4 x^2\right )\right )}+\frac {2 (-1+\log (x))}{x^2 \log ^2\left (\log ^2\left (4 x^2\right )\right )}\right ) \, dx\\ &=2 \int \frac {-1+\log (x)}{x^2 \log ^2\left (\log ^2\left (4 x^2\right )\right )} \, dx+16 \int \frac {\log (x)}{x^2 \log \left (4 x^2\right ) \log ^3\left (\log ^2\left (4 x^2\right )\right )} \, dx\\ &=2 \int \left (-\frac {1}{x^2 \log ^2\left (\log ^2\left (4 x^2\right )\right )}+\frac {\log (x)}{x^2 \log ^2\left (\log ^2\left (4 x^2\right )\right )}\right ) \, dx+16 \int \frac {\log (x)}{x^2 \log \left (4 x^2\right ) \log ^3\left (\log ^2\left (4 x^2\right )\right )} \, dx\\ &=-\left (2 \int \frac {1}{x^2 \log ^2\left (\log ^2\left (4 x^2\right )\right )} \, dx\right )+2 \int \frac {\log (x)}{x^2 \log ^2\left (\log ^2\left (4 x^2\right )\right )} \, dx+16 \int \frac {\log (x)}{x^2 \log \left (4 x^2\right ) \log ^3\left (\log ^2\left (4 x^2\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 18, normalized size = 1.00 \begin {gather*} -\frac {2 \log (x)}{x \log ^2\left (\log ^2\left (4 x^2\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 29, normalized size = 1.61 \begin {gather*} -\frac {2 \, \log \relax (x)}{x \log \left (4 \, \log \relax (2)^{2} + 8 \, \log \relax (2) \log \relax (x) + 4 \, \log \relax (x)^{2}\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.69, size = 257, normalized size = 14.28 \begin {gather*} -\frac {2 \, \log \relax (2)^{2} \log \left (4 \, x^{2}\right ) \log \relax (x) \log \left (\log \left (4 \, x^{2}\right )^{2}\right ) - \log \relax (2) \log \left (4 \, x^{2}\right )^{2} \log \relax (x) \log \left (\log \left (4 \, x^{2}\right )^{2}\right ) + 4 \, \log \relax (2) \log \left (4 \, x^{2}\right ) \log \relax (x)^{2} \log \left (\log \left (4 \, x^{2}\right )^{2}\right ) - \log \left (4 \, x^{2}\right )^{2} \log \relax (x)^{2} \log \left (\log \left (4 \, x^{2}\right )^{2}\right ) + 2 \, \log \left (4 \, x^{2}\right ) \log \relax (x)^{3} \log \left (\log \left (4 \, x^{2}\right )^{2}\right ) - 2 \, \log \relax (2)^{2} \log \left (4 \, x^{2}\right ) \log \left (\log \left (4 \, x^{2}\right )^{2}\right ) + \log \relax (2) \log \left (4 \, x^{2}\right )^{2} \log \left (\log \left (4 \, x^{2}\right )^{2}\right ) - 2 \, \log \relax (2) \log \left (4 \, x^{2}\right ) \log \relax (x) \log \left (\log \left (4 \, x^{2}\right )^{2}\right ) + 4 \, \log \relax (2) \log \left (4 \, x^{2}\right ) \log \relax (x) + 4 \, \log \left (4 \, x^{2}\right ) \log \relax (x)^{2}}{4 \, {\left (x \log \relax (2)^{2} \log \left (\log \left (4 \, x^{2}\right )^{2}\right )^{2} + 2 \, x \log \relax (2) \log \relax (x) \log \left (\log \left (4 \, x^{2}\right )^{2}\right )^{2} + x \log \relax (x)^{2} \log \left (\log \left (4 \, x^{2}\right )^{2}\right )^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.80, size = 459, normalized size = 25.50
method | result | size |
risch | \(\frac {8 \ln \relax (x )}{x \left (\pi \mathrm {csgn}\left (i \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (2)+4 i \ln \relax (x )\right )\right )^{2} \mathrm {csgn}\left (i \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (2)+4 i \ln \relax (x )\right )^{2}\right )-2 \pi \,\mathrm {csgn}\left (i \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (2)+4 i \ln \relax (x )\right )\right ) \mathrm {csgn}\left (i \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (2)+4 i \ln \relax (x )\right )^{2}\right )^{2}-\pi \mathrm {csgn}\left (i \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (2)+4 i \ln \relax (x )\right )^{2}\right )^{3}+2 \pi \mathrm {csgn}\left (i \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (2)+4 i \ln \relax (x )\right )^{2}\right )^{2}-2 \pi -4 i \ln \relax (2)+4 i \ln \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (2)+4 i \ln \relax (x )\right )\right )^{2}}\) | \(459\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 34, normalized size = 1.89 \begin {gather*} -\frac {\log \relax (x)}{2 \, {\left (x \log \relax (2)^{2} + 2 \, x \log \relax (2) \log \left (\log \relax (2) + \log \relax (x)\right ) + x \log \left (\log \relax (2) + \log \relax (x)\right )^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.06, size = 31, normalized size = 1.72 \begin {gather*} -\frac {2\,\ln \relax (x)}{x\,{\ln \left ({\ln \left (x^2\right )}^2+4\,\ln \relax (2)\,\ln \left (x^2\right )+4\,{\ln \relax (2)}^2\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 20, normalized size = 1.11 \begin {gather*} - \frac {2 \log {\relax (x )}}{x \log {\left (\left (2 \log {\relax (x )} + \log {\relax (4 )}\right )^{2} \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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