Optimal. Leaf size=19 \[ \frac {1}{2} x^2 \log (c x)-\frac {x^2}{4} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ \frac {1}{2} x^2 \log (c x)-\frac {x^2}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 15, normalized size = 0.79 \[ \frac {1}{2} \, x^{2} \log \left (c x\right ) - \frac {1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 15, normalized size = 0.79 \[ \frac {1}{2} \, x^{2} \log \left (c x\right ) - \frac {1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.84 \[ \frac {x^{2} \ln \left (c x \right )}{2}-\frac {x^{2}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 15, normalized size = 0.79 \[ \frac {1}{2} \, x^{2} \log \left (c x\right ) - \frac {1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 11, normalized size = 0.58 \[ \frac {x^2\,\left (\ln \left (c\,x\right )-\frac {1}{2}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.74 \[ \frac {x^{2} \log {\left (c x \right )}}{2} - \frac {x^{2}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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