Optimal. Leaf size=19 \[ \frac {1}{3} x^3 \log (c x)-\frac {x^3}{9} \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ \frac {1}{3} x^3 \log (c x)-\frac {x^3}{9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 15, normalized size = 0.79 \[ \frac {1}{3} \, x^{3} \log \left (c x\right ) - \frac {1}{9} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 15, normalized size = 0.79 \[ \frac {1}{3} \, x^{3} \log \left (c x\right ) - \frac {1}{9} \, x^{3} \]
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 \[ \frac {x^{3} \ln \left (c x \right )}{3}-\frac {x^{3}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 15, normalized size = 0.79 \[ \frac {1}{3} \, x^{3} \log \left (c x\right ) - \frac {1}{9} \, x^{3} \]
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 \[ \frac {x^3\,\left (\ln \left (c\,x\right )-\frac {1}{3}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 14, normalized size = 0.74 \[ \frac {x^{3} \log {\left (c x \right )}}{3} - \frac {x^{3}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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