Optimal. Leaf size=11 \[ \frac {1}{2} \log ^2(\log (6 x)) \]
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Rubi [A] time = 0.03, antiderivative size = 11, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ \frac {1}{2} \log ^2(\log (6 x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 9, normalized size = 0.82 \[ \frac {1}{2} \, \log \left (\log \left (6 \, x\right )\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 9, normalized size = 0.82 \[ \frac {1}{2} \, \log \left (\log \left (6 \, x\right )\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 10, normalized size = 0.91 \[ \frac {\ln \left (\ln \left (6 x \right )\right )^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 9, normalized size = 0.82 \[ \frac {1}{2} \, \log \left (\log \left (6 \, x\right )\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.52, size = 9, normalized size = 0.82 \[ \frac {{\ln \left (\ln \left (6\,x\right )\right )}^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 8, normalized size = 0.73 \[ \frac {\log {\left (\log {\left (6 x \right )} \right )}^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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