Optimal. Leaf size=17 \[ -\frac {x^2}{4}+\frac {1}{2} x^2 \log (x) \]
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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 = {2341}
\begin {gather*} \frac {1}{2} x^2 \log (x)-\frac {x^2}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
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 \begin {gather*} -\frac {x^2}{4}+\frac {1}{2} x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.00, size = 14, normalized size = 0.82
method | result | size |
default | \(-\frac {x^{2}}{4}+\frac {x^{2} \ln \left (x \right )}{2}\) | \(14\) |
norman | \(-\frac {x^{2}}{4}+\frac {x^{2} \ln \left (x \right )}{2}\) | \(14\) |
risch | \(-\frac {x^{2}}{4}+\frac {x^{2} \ln \left (x \right )}{2}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.24, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{2} \, x^{2} \log \left (x\right ) - \frac {1}{4} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.80, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{2} \, x^{2} \log \left (x\right ) - \frac {1}{4} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 12, normalized size = 0.71 \begin {gather*} \frac {x^{2} \log {\left (x \right )}}{2} - \frac {x^{2}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.60, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{2} \, x^{2} \log \left (x\right ) - \frac {1}{4} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.00, size = 9, normalized size = 0.53 \begin {gather*} \frac {x^2\,\left (\ln \left (x\right )-\frac {1}{2}\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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