Optimal. Leaf size=10 \[ \frac{1}{3} \log ^3(c x) \]
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Rubi [A] time = 0.0121408, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {2302, 30} \[ \frac{1}{3} \log ^3(c x) \]
Antiderivative was successfully verified.
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Rule 2302
Rule 30
Rubi steps
\begin{align*} \int \frac{\log ^2(c x)}{x} \, dx &=\operatorname{Subst}\left (\int x^2 \, dx,x,\log (c x)\right )\\ &=\frac{1}{3} \log ^3(c x)\\ \end{align*}
Mathematica [A] time = 0.0009469, size = 10, normalized size = 1. \[ \frac{1}{3} \log ^3(c x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.035, size = 9, normalized size = 0.9 \begin{align*}{\frac{ \left ( \ln \left ( cx \right ) \right ) ^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.968349, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{3} \, \log \left (c x\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.790002, size = 22, normalized size = 2.2 \begin{align*} \frac{1}{3} \, \log \left (c x\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.086911, size = 7, normalized size = 0.7 \begin{align*} \frac{\log{\left (c x \right )}^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10985, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{3} \, \log \left (c x\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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