Optimal. Leaf size=27 \[ -\frac{x^2}{2}-\frac{1}{6} \left (2-3 x^2\right ) \log \left (2-3 x^2\right ) \]
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Rubi [A] time = 0.0212735, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.3, Rules used = {2454, 2389, 2295} \[ -\frac{x^2}{2}-\frac{1}{6} \left (2-3 x^2\right ) \log \left (2-3 x^2\right ) \]
Antiderivative was successfully verified.
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Rule 2454
Rule 2389
Rule 2295
Rubi steps
\begin{align*} \int x \log \left (2-3 x^2\right ) \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \log (2-3 x) \, dx,x,x^2\right )\\ &=-\left (\frac{1}{6} \operatorname{Subst}\left (\int \log (x) \, dx,x,2-3 x^2\right )\right )\\ &=-\frac{x^2}{2}-\frac{1}{6} \left (2-3 x^2\right ) \log \left (2-3 x^2\right )\\ \end{align*}
Mathematica [A] time = 0.0037477, size = 26, normalized size = 0.96 \[ \frac{1}{6} \left (\left (3 x^2-2\right ) \log \left (2-3 x^2\right )-3 x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 0.9 \begin{align*} -{\frac{ \left ( -3\,{x}^{2}+2 \right ) \ln \left ( -3\,{x}^{2}+2 \right ) }{6}}-{\frac{{x}^{2}}{2}}+{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06472, size = 32, normalized size = 1.19 \begin{align*} -\frac{1}{2} \, x^{2} + \frac{1}{6} \,{\left (3 \, x^{2} - 2\right )} \log \left (-3 \, x^{2} + 2\right ) + \frac{1}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.84247, size = 59, normalized size = 2.19 \begin{align*} -\frac{1}{2} \, x^{2} + \frac{1}{6} \,{\left (3 \, x^{2} - 2\right )} \log \left (-3 \, x^{2} + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.126375, size = 27, normalized size = 1. \begin{align*} \frac{x^{2} \log{\left (2 - 3 x^{2} \right )}}{2} - \frac{x^{2}}{2} - \frac{\log{\left (3 x^{2} - 2 \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.33089, size = 32, normalized size = 1.19 \begin{align*} -\frac{1}{2} \, x^{2} + \frac{1}{6} \,{\left (3 \, x^{2} - 2\right )} \log \left (-3 \, x^{2} + 2\right ) + \frac{1}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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