Optimal. Leaf size=10 \[ -\frac{1}{2 \log ^2(c x)} \]
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Rubi [A] time = 0.0121339, 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} \[ -\frac{1}{2 \log ^2(c x)} \]
Antiderivative was successfully verified.
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Rule 2302
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x \log ^3(c x)} \, dx &=\operatorname{Subst}\left (\int \frac{1}{x^3} \, dx,x,\log (c x)\right )\\ &=-\frac{1}{2 \log ^2(c x)}\\ \end{align*}
Mathematica [A] time = 0.0010784, size = 10, normalized size = 1. \[ -\frac{1}{2 \log ^2(c x)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.033, size = 9, normalized size = 0.9 \begin{align*} -{\frac{1}{2\, \left ( \ln \left ( cx \right ) \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10878, size = 11, normalized size = 1.1 \begin{align*} -\frac{1}{2 \, \log \left (c x\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.860774, size = 23, normalized size = 2.3 \begin{align*} -\frac{1}{2 \, \log \left (c x\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.090014, size = 10, normalized size = 1. \begin{align*} - \frac{1}{2 \log{\left (c x \right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11042, size = 11, normalized size = 1.1 \begin{align*} -\frac{1}{2 \, \log \left (c x\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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