Optimal. Leaf size=18 \[ \log ^2\left (9+3 x-\frac {\log (x \log (4))}{x^2}\right ) \]
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Rubi [A] time = 0.33, antiderivative size = 25, normalized size of antiderivative = 1.39, number of steps used = 1, number of rules used = 5, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {6741, 12, 6742, 6684, 6686} \begin {gather*} \log ^2\left (\frac {3 x^3+9 x^2-\log (x \log (4))}{x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6686
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log ^2\left (\frac {9 x^2+3 x^3-\log (x \log (4))}{x^2}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 18, normalized size = 1.00 \begin {gather*} \log ^2\left (9+3 x-\frac {\log (x \log (4))}{x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 26, normalized size = 1.44 \begin {gather*} \log \left (\frac {3 \, x^{3} + 9 \, x^{2} - \log \left (2 \, x \log \relax (2)\right )}{x^{2}}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.21, size = 79, normalized size = 4.39 \begin {gather*} 2 \, {\left (\log \left (-3 \, x^{3} - 9 \, x^{2} + \log \relax (2) + \log \relax (x) + \log \left (\log \relax (2)\right )\right ) - 2 \, \log \relax (x)\right )} \log \left (3 \, x^{3} + 9 \, x^{2} - \log \relax (2) - \log \left (x \log \relax (2)\right )\right ) - \log \left (-3 \, x^{3} - 9 \, x^{2} + \log \relax (2) + \log \relax (x) + \log \left (\log \relax (2)\right )\right )^{2} + 4 \, \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {\left (-4 \ln \left (2 x \ln \relax (2)\right )-6 x^{3}+2\right ) \ln \left (\frac {-\ln \left (2 x \ln \relax (2)\right )+3 x^{3}+9 x^{2}}{x^{2}}\right )}{x \ln \left (2 x \ln \relax (2)\right )-3 x^{4}-9 x^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.48, size = 103, normalized size = 5.72 \begin {gather*} -\log \left (-3 \, x^{3} - 9 \, x^{2} + \log \relax (2) + \log \relax (x) + \log \left (\log \relax (2)\right )\right )^{2} + 4 \, \log \left (-3 \, x^{3} - 9 \, x^{2} + \log \relax (2) + \log \relax (x) + \log \left (\log \relax (2)\right )\right ) \log \relax (x) - 4 \, \log \relax (x)^{2} + 2 \, {\left (\log \left (-3 \, x^{3} - 9 \, x^{2} + \log \relax (2) + \log \relax (x) + \log \left (\log \relax (2)\right )\right ) - 2 \, \log \relax (x)\right )} \log \left (\frac {3 \, x^{3} + 9 \, x^{2} - \log \left (2 \, x \log \relax (2)\right )}{x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.00, size = 26, normalized size = 1.44 \begin {gather*} {\ln \left (\frac {9\,x^2-\ln \left (2\,x\,\ln \relax (2)\right )+3\,x^3}{x^2}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 24, normalized size = 1.33 \begin {gather*} \log {\left (\frac {3 x^{3} + 9 x^{2} - \log {\left (2 x \log {\relax (2 )} \right )}}{x^{2}} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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