Optimal. Leaf size=19 \[ \frac{1}{2} x^2 \log (c x)-\frac{x^2}{4} \]
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Rubi [A] time = 0.0039277, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {2304} \[ \frac{1}{2} x^2 \log (c x)-\frac{x^2}{4} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin{align*} \int x \log (c x) \, dx &=-\frac{x^2}{4}+\frac{1}{2} x^2 \log (c x)\\ \end{align*}
Mathematica [A] time = 0.0006873, size = 19, normalized size = 1. \[ \frac{1}{2} x^2 \log (c x)-\frac{x^2}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.037, size = 16, normalized size = 0.8 \begin{align*} -{\frac{{x}^{2}}{4}}+{\frac{{x}^{2}\ln \left ( cx \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.960376, size = 20, normalized size = 1.05 \begin{align*} \frac{1}{2} \, x^{2} \log \left (c x\right ) - \frac{1}{4} \, x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.815068, size = 38, normalized size = 2. \begin{align*} \frac{1}{2} \, x^{2} \log \left (c x\right ) - \frac{1}{4} \, x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.087329, size = 14, normalized size = 0.74 \begin{align*} \frac{x^{2} \log{\left (c x \right )}}{2} - \frac{x^{2}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10545, size = 20, normalized size = 1.05 \begin{align*} \frac{1}{2} \, x^{2} \log \left (c x\right ) - \frac{1}{4} \, x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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