Optimal. Leaf size=23 \[ \frac {5}{2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )} \]
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Rubi [F] time = 2.30, 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 {-10 \log (5 x)+\left (-5 x-10 x^2 \log (5 x)\right ) \log \left (x^2\right )-5 \log \left (x^2\right ) \log \left (e^{x^2} \log \left (x^2\right )\right )}{\left (4 x+4 x^2+x^3\right ) \log \left (x^2\right )+\left (4 x+2 x^2\right ) \log (5 x) \log \left (x^2\right ) \log \left (e^{x^2} \log \left (x^2\right )\right )+x \log ^2(5 x) \log \left (x^2\right ) \log ^2\left (e^{x^2} \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 {5 \left (-2 \log (5 x) \left (1+x^2 \log \left (x^2\right )\right )-\log \left (x^2\right ) \left (x+\log \left (e^{x^2} \log \left (x^2\right )\right )\right )\right )}{x \log \left (x^2\right ) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2} \, dx\\ &=5 \int \frac {-2 \log (5 x) \left (1+x^2 \log \left (x^2\right )\right )-\log \left (x^2\right ) \left (x+\log \left (e^{x^2} \log \left (x^2\right )\right )\right )}{x \log \left (x^2\right ) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2} \, dx\\ &=5 \int \left (\frac {-2 \log ^2(5 x)+2 \log \left (x^2\right )+x \log \left (x^2\right )-x \log (5 x) \log \left (x^2\right )-2 x^2 \log ^2(5 x) \log \left (x^2\right )}{x \log (5 x) \log \left (x^2\right ) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2}-\frac {1}{x \log (5 x) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )}\right ) \, dx\\ &=5 \int \frac {-2 \log ^2(5 x)+2 \log \left (x^2\right )+x \log \left (x^2\right )-x \log (5 x) \log \left (x^2\right )-2 x^2 \log ^2(5 x) \log \left (x^2\right )}{x \log (5 x) \log \left (x^2\right ) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2} \, dx-5 \int \frac {1}{x \log (5 x) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )} \, dx\\ &=-\left (5 \int \frac {1}{x \log (5 x) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )} \, dx\right )+5 \int \left (-\frac {1}{\left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2}+\frac {1}{\log (5 x) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2}+\frac {2}{x \log (5 x) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2}-\frac {2 x \log (5 x)}{\left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2}-\frac {2 \log (5 x)}{x \log \left (x^2\right ) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2}\right ) \, dx\\ &=-\left (5 \int \frac {1}{\left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2} \, dx\right )+5 \int \frac {1}{\log (5 x) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2} \, dx-5 \int \frac {1}{x \log (5 x) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )} \, dx+10 \int \frac {1}{x \log (5 x) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2} \, dx-10 \int \frac {x \log (5 x)}{\left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2} \, dx-10 \int \frac {\log (5 x)}{x \log \left (x^2\right ) \left (2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.72, size = 23, normalized size = 1.00 \begin {gather*} \frac {5}{2+x+\log (5 x) \log \left (e^{x^2} \log \left (x^2\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 32, normalized size = 1.39 \begin {gather*} \frac {5}{\log \left (-2 \, e^{\left (x^{2}\right )} \log \relax (5) + 2 \, e^{\left (x^{2}\right )} \log \left (5 \, x\right )\right ) \log \left (5 \, x\right ) + x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.38, size = 697, normalized size = 30.30 result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {-5 \ln \left (x^{2}\right ) \ln \left ({\mathrm e}^{x^{2}} \ln \left (x^{2}\right )\right )+\left (-10 x^{2} \ln \left (5 x \right )-5 x \right ) \ln \left (x^{2}\right )-10 \ln \left (5 x \right )}{x \ln \left (5 x \right )^{2} \ln \left (x^{2}\right ) \ln \left ({\mathrm e}^{x^{2}} \ln \left (x^{2}\right )\right )^{2}+\left (2 x^{2}+4 x \right ) \ln \left (5 x \right ) \ln \left (x^{2}\right ) \ln \left ({\mathrm e}^{x^{2}} \ln \left (x^{2}\right )\right )+\left (x^{3}+4 x^{2}+4 x \right ) \ln \left (x^{2}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 36, normalized size = 1.57 \begin {gather*} \frac {5}{x^{2} \log \relax (5) + \log \relax (5) \log \relax (2) + {\left (x^{2} + \log \relax (2)\right )} \log \relax (x) + {\left (\log \relax (5) + \log \relax (x)\right )} \log \left (\log \relax (x)\right ) + x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.42, size = 22, normalized size = 0.96 \begin {gather*} \frac {5}{x+\ln \left (5\,x\right )\,\ln \left (\ln \left (x^2\right )\,{\mathrm {e}}^{x^2}\right )+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.59, size = 26, normalized size = 1.13 \begin {gather*} \frac {5}{x + \log {\left (5 x \right )} \log {\left (\left (2 \log {\left (5 x \right )} - \log {\left (25 \right )}\right ) e^{x^{2}} \right )} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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