Optimal. Leaf size=8 \[ -\frac{1}{\log (c x)} \]
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Rubi [A] time = 0.0118305, antiderivative size = 8, 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} \[ -\frac{1}{\log (c x)} \]
Antiderivative was successfully verified.
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Rule 2302
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x \log ^2(c x)} \, dx &=\operatorname{Subst}\left (\int \frac{1}{x^2} \, dx,x,\log (c x)\right )\\ &=-\frac{1}{\log (c x)}\\ \end{align*}
Mathematica [A] time = 0.0010445, size = 8, normalized size = 1. \[ -\frac{1}{\log (c x)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.033, size = 9, normalized size = 1.1 \begin{align*} - \left ( \ln \left ( cx \right ) \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09388, size = 11, normalized size = 1.38 \begin{align*} -\frac{1}{\log \left (c x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.768227, size = 18, normalized size = 2.25 \begin{align*} -\frac{1}{\log \left (c x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.082636, size = 7, normalized size = 0.88 \begin{align*} - \frac{1}{\log{\left (c x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10535, size = 11, normalized size = 1.38 \begin{align*} -\frac{1}{\log \left (c x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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