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 = 0.02, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.300, 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 2295
Rule 2389
Rule 2454
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*}
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Mathematica [A] time = 0.00, 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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fricas [A] time = 0.47, size = 23, normalized size = 0.85 \[ -\frac {1}{2} \, x^{2} + \frac {1}{6} \, {\left (3 \, x^{2} - 2\right )} \log \left (-3 \, x^{2} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 24, normalized size = 0.89 \[ -\frac {1}{2} \, x^{2} + \frac {1}{6} \, {\left (3 \, x^{2} - 2\right )} \log \left (-3 \, x^{2} + 2\right ) + \frac {1}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 25, normalized size = 0.93 \[ -\frac {x^{2}}{2}-\frac {\left (-3 x^{2}+2\right ) \ln \left (-3 x^{2}+2\right )}{6}+\frac {1}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 24, normalized size = 0.89 \[ -\frac {1}{2} \, x^{2} + \frac {1}{6} \, {\left (3 \, x^{2} - 2\right )} \log \left (-3 \, x^{2} + 2\right ) + \frac {1}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 25, normalized size = 0.93 \[ x^2\,\left (\frac {\ln \left (2-3\,x^2\right )}{2}-\frac {1}{2}\right )-\frac {\ln \left (x^2-\frac {2}{3}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 27, normalized size = 1.00 \[ \frac {x^{2} \log {\left (2 - 3 x^{2} \right )}}{2} - \frac {x^{2}}{2} - \frac {\log {\left (3 x^{2} - 2 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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