Optimal. Leaf size=19 \[ -\frac {\log (c x)}{2 x^2}-\frac {1}{4 x^2} \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ -\frac {\log (c x)}{2 x^2}-\frac {1}{4 x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 13, normalized size = 0.68 \[ -\frac {2 \, \log \left (c x\right ) + 1}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 15, normalized size = 0.79 \[ -\frac {\log \left (c x\right )}{2 \, x^{2}} - \frac {1}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.84 \[ -\frac {\ln \left (c x \right )}{2 x^{2}}-\frac {1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 15, normalized size = 0.79 \[ -\frac {\log \left (c x\right )}{2 \, x^{2}} - \frac {1}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 0.58 \[ -\frac {\ln \left (c\,x\right )+\frac {1}{2}}{2\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 0.89 \[ - \frac {\log {\left (c x \right )}}{2 x^{2}} - \frac {1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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