Optimal. Leaf size=10 \[ \frac {1}{4} \log ^4(c x) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2302, 30} \[ \frac {1}{4} \log ^4(c x) \]
Antiderivative was successfully verified.
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Rule 30
Rule 2302
Rubi steps
\begin {align*} \int \frac {\log ^3(c x)}{x} \, dx &=\operatorname {Subst}\left (\int x^3 \, dx,x,\log (c x)\right )\\ &=\frac {1}{4} \log ^4(c x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \[ \frac {1}{4} \log ^4(c x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 8, normalized size = 0.80 \[ \frac {1}{4} \, \log \left (c x\right )^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 8, normalized size = 0.80 \[ \frac {1}{4} \, \log \left (c x\right )^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 9, normalized size = 0.90 \[ \frac {\ln \left (c x \right )^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 8, normalized size = 0.80 \[ \frac {1}{4} \, \log \left (c x\right )^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.53, size = 8, normalized size = 0.80 \[ \frac {{\ln \left (c\,x\right )}^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 7, normalized size = 0.70 \[ \frac {\log {\left (c x \right )}^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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