Optimal. Leaf size=22 \[ 1-\log (x)+\frac {12}{x^3 \log \left (-x+\log \left (x^2\right )\right )} \]
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Rubi [F] time = 0.82, 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 {-24+12 x+\left (36 x-36 \log \left (x^2\right )\right ) \log \left (-x+\log \left (x^2\right )\right )+\left (x^4-x^3 \log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )}{\left (-x^5+x^4 \log \left (x^2\right )\right ) \log ^2\left (-x+\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 {-24+12 x+\left (36 x-36 \log \left (x^2\right )\right ) \log \left (-x+\log \left (x^2\right )\right )+\left (x^4-x^3 \log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )}{x^4 \left (-x+\log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )} \, dx\\ &=\int \frac {-x^3-\frac {12 (-2+x)}{\left (x-\log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )}-\frac {36}{\log \left (-x+\log \left (x^2\right )\right )}}{x^4} \, dx\\ &=\int \left (-\frac {1}{x}-\frac {12 (-2+x)}{x^4 \left (x-\log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )}-\frac {36}{x^4 \log \left (-x+\log \left (x^2\right )\right )}\right ) \, dx\\ &=-\log (x)-12 \int \frac {-2+x}{x^4 \left (x-\log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )} \, dx-36 \int \frac {1}{x^4 \log \left (-x+\log \left (x^2\right )\right )} \, dx\\ &=-\log (x)-12 \int \left (-\frac {2}{x^4 \left (x-\log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )}+\frac {1}{x^3 \left (x-\log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )}\right ) \, dx-36 \int \frac {1}{x^4 \log \left (-x+\log \left (x^2\right )\right )} \, dx\\ &=-\log (x)-12 \int \frac {1}{x^3 \left (x-\log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )} \, dx+24 \int \frac {1}{x^4 \left (x-\log \left (x^2\right )\right ) \log ^2\left (-x+\log \left (x^2\right )\right )} \, dx-36 \int \frac {1}{x^4 \log \left (-x+\log \left (x^2\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.31, size = 21, normalized size = 0.95 \begin {gather*} -\log (x)+\frac {12}{x^3 \log \left (-x+\log \left (x^2\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 35, normalized size = 1.59 \begin {gather*} -\frac {x^{3} \log \left (x^{2}\right ) \log \left (-x + \log \left (x^{2}\right )\right ) - 24}{2 \, x^{3} \log \left (-x + \log \left (x^{2}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 21, normalized size = 0.95 \begin {gather*} \frac {12}{x^{3} \log \left (-x + \log \left (x^{2}\right )\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (-x^{3} \ln \left (x^{2}\right )+x^{4}\right ) \ln \left (\ln \left (x^{2}\right )-x \right )^{2}+\left (-36 \ln \left (x^{2}\right )+36 x \right ) \ln \left (\ln \left (x^{2}\right )-x \right )+12 x -24}{\left (x^{4} \ln \left (x^{2}\right )-x^{5}\right ) \ln \left (\ln \left (x^{2}\right )-x \right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 21, normalized size = 0.95 \begin {gather*} \frac {12}{x^{3} \log \left (-x + 2 \, \log \relax (x)\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.72, size = 52, normalized size = 2.36 \begin {gather*} \frac {36}{2\,x^2-x^3}-\frac {36\,x}{2\,x^3-x^4}-\ln \relax (x)+\frac {12}{x^3\,\ln \left (\ln \left (x^2\right )-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 15, normalized size = 0.68 \begin {gather*} - \log {\relax (x )} + \frac {12}{x^{3} \log {\left (- x + \log {\left (x^{2} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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