Optimal. Leaf size=17 \[ \frac {1}{2} x^2 \log (x)-\frac {x^2}{4} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2304} \[ \frac {1}{2} x^2 \log (x)-\frac {x^2}{4} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin {align*} \int x \log (x) \, dx &=-\frac {x^2}{4}+\frac {1}{2} x^2 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {1}{2} x^2 \log (x)-\frac {x^2}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 13, normalized size = 0.76 \[ \frac {1}{2} \, x^{2} \log \relax (x) - \frac {1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.10, size = 13, normalized size = 0.76 \[ \frac {1}{2} \, x^{2} \log \relax (x) - \frac {1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.82 \[ \frac {x^{2} \ln \relax (x )}{2}-\frac {x^{2}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 13, normalized size = 0.76 \[ \frac {1}{2} \, x^{2} \log \relax (x) - \frac {1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 9, normalized size = 0.53 \[ \frac {x^2\,\left (\ln \relax (x)-\frac {1}{2}\right )}{2} \]
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 \[ \frac {x^{2} \log {\relax (x )}}{2} - \frac {x^{2}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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