Optimal. Leaf size=19 \[ -\frac{\log (c x)}{2 x^2}-\frac{1}{4 x^2} \]
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Rubi [A] time = 0.0066814, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {2304} \[ -\frac{\log (c x)}{2 x^2}-\frac{1}{4 x^2} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin{align*} \int \frac{\log (c x)}{x^3} \, dx &=-\frac{1}{4 x^2}-\frac{\log (c x)}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0008228, size = 19, normalized size = 1. \[ -\frac{\log (c x)}{2 x^2}-\frac{1}{4 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.035, size = 16, normalized size = 0.8 \begin{align*} -{\frac{1}{4\,{x}^{2}}}-{\frac{\ln \left ( cx \right ) }{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.97228, size = 20, normalized size = 1.05 \begin{align*} -\frac{\log \left (c x\right )}{2 \, x^{2}} - \frac{1}{4 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.826076, size = 36, normalized size = 1.89 \begin{align*} -\frac{2 \, \log \left (c x\right ) + 1}{4 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.131911, size = 17, normalized size = 0.89 \begin{align*} - \frac{\log{\left (c x \right )}}{2 x^{2}} - \frac{1}{4 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09793, size = 20, normalized size = 1.05 \begin{align*} -\frac{\log \left (c x\right )}{2 \, x^{2}} - \frac{1}{4 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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