Optimal. Leaf size=19 \[ \frac{1}{3} x^3 \log (c x)-\frac{x^3}{9} \]
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Rubi [A] time = 0.0066558, 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} \[ \frac{1}{3} x^3 \log (c x)-\frac{x^3}{9} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin{align*} \int x^2 \log (c x) \, dx &=-\frac{x^3}{9}+\frac{1}{3} x^3 \log (c x)\\ \end{align*}
Mathematica [A] time = 0.0009417, size = 19, normalized size = 1. \[ \frac{1}{3} x^3 \log (c x)-\frac{x^3}{9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.036, size = 16, normalized size = 0.8 \begin{align*} -{\frac{{x}^{3}}{9}}+{\frac{{x}^{3}\ln \left ( cx \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959366, size = 20, normalized size = 1.05 \begin{align*} \frac{1}{3} \, x^{3} \log \left (c x\right ) - \frac{1}{9} \, x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.838674, size = 38, normalized size = 2. \begin{align*} \frac{1}{3} \, x^{3} \log \left (c x\right ) - \frac{1}{9} \, x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.097191, size = 14, normalized size = 0.74 \begin{align*} \frac{x^{3} \log{\left (c x \right )}}{3} - \frac{x^{3}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08101, size = 20, normalized size = 1.05 \begin{align*} \frac{1}{3} \, x^{3} \log \left (c x\right ) - \frac{1}{9} \, x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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