Optimal. Leaf size=28 \[ \frac {x^2}{4}+\frac {1}{2} x^2 \log ^2(x)-\frac {1}{2} x^2 \log (x) \]
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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 = {2305, 2304} \[ \frac {x^2}{4}+\frac {1}{2} x^2 \log ^2(x)-\frac {1}{2} x^2 \log (x) \]
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
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 \[ \frac {x^2}{4}+\frac {1}{2} x^2 \log ^2(x)-\frac {1}{2} x^2 \log (x) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x \log ^2(x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.92, size = 22, normalized size = 0.79 \[ \frac {1}{2} \, x^{2} \log \relax (x)^{2} - \frac {1}{2} \, x^{2} \log \relax (x) + \frac {1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 22, normalized size = 0.79 \[ \frac {1}{2} \, x^{2} \log \relax (x)^{2} - \frac {1}{2} \, x^{2} \log \relax (x) + \frac {1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 23, normalized size = 0.82
method | result | size |
default | \(\frac {x^{2}}{4}-\frac {x^{2} \ln \relax (x )}{2}+\frac {x^{2} \ln \relax (x )^{2}}{2}\) | \(23\) |
norman | \(\frac {x^{2}}{4}-\frac {x^{2} \ln \relax (x )}{2}+\frac {x^{2} \ln \relax (x )^{2}}{2}\) | \(23\) |
risch | \(\frac {x^{2}}{4}-\frac {x^{2} \ln \relax (x )}{2}+\frac {x^{2} \ln \relax (x )^{2}}{2}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 17, normalized size = 0.61 \[ \frac {1}{4} \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} \]
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 \[ \frac {x^2\,\left (2\,{\ln \relax (x)}^2-2\,\ln \relax (x)+1\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 22, normalized size = 0.79 \[ \frac {x^{2} \log {\relax (x )}^{2}}{2} - \frac {x^{2} \log {\relax (x )}}{2} + \frac {x^{2}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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