Optimal. Leaf size=28 \[ \frac {x^2}{4}-\frac {1}{2} x^2 \log (x)+\frac {1}{2} x^2 \log ^2(x) \]
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Rubi [A]
time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2342, 2341}
\begin {gather*} \frac {x^2}{4}+\frac {1}{2} x^2 \log ^2(x)-\frac {1}{2} x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
Rule 2342
Rubi steps
\begin {align*} \int x \log ^2(x) \, dx &=\frac {1}{2} x^2 \log ^2(x)-\int x \log (x) \, dx\\ &=\frac {x^2}{4}-\frac {1}{2} x^2 \log (x)+\frac {1}{2} x^2 \log ^2(x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} \frac {x^2}{4}-\frac {1}{2} x^2 \log (x)+\frac {1}{2} x^2 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.00, size = 23, normalized size = 0.82
method | result | size |
default | \(\frac {x^{2}}{4}-\frac {x^{2} \ln \left (x \right )}{2}+\frac {x^{2} \ln \left (x \right )^{2}}{2}\) | \(23\) |
norman | \(\frac {x^{2}}{4}-\frac {x^{2} \ln \left (x \right )}{2}+\frac {x^{2} \ln \left (x \right )^{2}}{2}\) | \(23\) |
risch | \(\frac {x^{2}}{4}-\frac {x^{2} \ln \left (x \right )}{2}+\frac {x^{2} \ln \left (x \right )^{2}}{2}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.79, size = 17, normalized size = 0.61 \begin {gather*} \frac {1}{4} \, {\left (2 \, \log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 1\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.68, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{2} \, x^{2} \log \left (x\right )^{2} - \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 = 0.03, size = 22, normalized size = 0.79 \begin {gather*} \frac {x^{2} \log {\left (x \right )}^{2}}{2} - \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 = 0.46, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{2} \, x^{2} \log \left (x\right )^{2} - \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 = 0.03, size = 17, normalized size = 0.61 \begin {gather*} \frac {x^2\,\left (2\,{\ln \left (x\right )}^2-2\,\ln \left (x\right )+1\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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