Optimal. Leaf size=17 \[ \frac {1}{3} x^3 \log (x)-\frac {x^3}{9} \]
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Rubi [A] time = 0.01, antiderivative size = 17, 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} \[ \frac {1}{3} x^3 \log (x)-\frac {x^3}{9} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin {align*} \int x^2 \log (x) \, dx &=-\frac {x^3}{9}+\frac {1}{3} x^3 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {1}{3} x^3 \log (x)-\frac {x^3}{9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 13, normalized size = 0.76 \[ \frac {1}{3} \, x^{3} \log \relax (x) - \frac {1}{9} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.11, size = 13, normalized size = 0.76 \[ \frac {1}{3} \, x^{3} \log \relax (x) - \frac {1}{9} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 14, normalized size = 0.82 \[ \frac {x^{3} \ln \relax (x )}{3}-\frac {x^{3}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 13, normalized size = 0.76 \[ \frac {1}{3} \, x^{3} \log \relax (x) - \frac {1}{9} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 9, normalized size = 0.53 \[ \frac {x^3\,\left (\ln \relax (x)-\frac {1}{3}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.71 \[ \frac {x^{3} \log {\relax (x )}}{3} - \frac {x^{3}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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