Optimal. Leaf size=19 \[ \frac{1}{4} x^4 \log (c x)-\frac{x^4}{16} \]
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Rubi [A] time = 0.0075869, 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} \[ \frac{1}{4} x^4 \log (c x)-\frac{x^4}{16} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin{align*} \int x^3 \log (c x) \, dx &=-\frac{x^4}{16}+\frac{1}{4} x^4 \log (c x)\\ \end{align*}
Mathematica [A] time = 0.001066, size = 19, normalized size = 1. \[ \frac{1}{4} x^4 \log (c x)-\frac{x^4}{16} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.037, size = 16, normalized size = 0.8 \begin{align*} -{\frac{{x}^{4}}{16}}+{\frac{{x}^{4}\ln \left ( cx \right ) }{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.954678, size = 20, normalized size = 1.05 \begin{align*} \frac{1}{4} \, x^{4} \log \left (c x\right ) - \frac{1}{16} \, x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.787972, size = 39, normalized size = 2.05 \begin{align*} \frac{1}{4} \, x^{4} \log \left (c x\right ) - \frac{1}{16} \, x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.091888, size = 14, normalized size = 0.74 \begin{align*} \frac{x^{4} \log{\left (c x \right )}}{4} - \frac{x^{4}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07294, size = 20, normalized size = 1.05 \begin{align*} \frac{1}{4} \, x^{4} \log \left (c x\right ) - \frac{1}{16} \, x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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