Optimal. Leaf size=11 \[ \frac{1}{2} \log ^2(\log (6 x)) \]
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Rubi [A] time = 0.0283252, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {2301} \[ \frac{1}{2} \log ^2(\log (6 x)) \]
Antiderivative was successfully verified.
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Rule 2301
Rubi steps
\begin{align*} \int \frac{\log (\log (6 x))}{x \log (6 x)} \, dx &=\operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,\log (6 x)\right )\\ &=\frac{1}{2} \log ^2(\log (6 x))\\ \end{align*}
Mathematica [A] time = 0.0039504, size = 11, normalized size = 1. \[ \frac{1}{2} \log ^2(\log (6 x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 10, normalized size = 0.9 \begin{align*}{\frac{ \left ( \ln \left ( \ln \left ( 6\,x \right ) \right ) \right ) ^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09572, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{2} \, \log \left (\log \left (6 \, x\right )\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.08825, size = 28, normalized size = 2.55 \begin{align*} \frac{1}{2} \, \log \left (\log \left (6 \, x\right )\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.290454, size = 8, normalized size = 0.73 \begin{align*} \frac{\log{\left (\log{\left (6 x \right )} \right )}^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.30393, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{2} \, \log \left (\log \left (6 \, x\right )\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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