Optimal. Leaf size=25 \[ -\frac {x^2}{4}+\frac {1}{2} x^2 \log (x)+\frac {\log ^2(x)}{2} \]
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Rubi [A]
time = 0.02, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 5, number of rules used = 5, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.625, Rules used = {1607, 14, 2393,
2338, 2341} \begin {gather*} -\frac {x^2}{4}+\frac {1}{2} x^2 \log (x)+\frac {\log ^2(x)}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 1607
Rule 2338
Rule 2341
Rule 2393
Rubi steps
\begin {align*} \int \left (\frac {1}{x}+x\right ) \log (x) \, dx &=\int \frac {\left (1+x^2\right ) \log (x)}{x} \, dx\\ &=\int \left (\frac {\log (x)}{x}+x \log (x)\right ) \, dx\\ &=\int \frac {\log (x)}{x} \, dx+\int x \log (x) \, dx\\ &=-\frac {x^2}{4}+\frac {1}{2} x^2 \log (x)+\frac {\log ^2(x)}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} -\frac {x^2}{4}+\frac {1}{2} x^2 \log (x)+\frac {\log ^2(x)}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 20, normalized size = 0.80
method | result | size |
default | \(-\frac {x^{2}}{4}+\frac {x^{2} \ln \left (x \right )}{2}+\frac {\ln \left (x \right )^{2}}{2}\) | \(20\) |
norman | \(-\frac {x^{2}}{4}+\frac {x^{2} \ln \left (x \right )}{2}+\frac {\ln \left (x \right )^{2}}{2}\) | \(20\) |
risch | \(-\frac {x^{2}}{4}+\frac {x^{2} \ln \left (x \right )}{2}+\frac {\ln \left (x \right )^{2}}{2}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.50, size = 24, normalized size = 0.96 \begin {gather*} -\frac {1}{4} \, x^{2} + \frac {1}{2} \, {\left (x^{2} + 2 \, \log \left (x\right )\right )} \log \left (x\right ) - \frac {1}{2} \, \log \left (x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.20, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{2} \, x^{2} \log \left (x\right ) - \frac {1}{4} \, x^{2} + \frac {1}{2} \, \log \left (x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 19, normalized size = 0.76 \begin {gather*} \frac {x^{2} \log {\left (x \right )}}{2} - \frac {x^{2}}{4} + \frac {\log {\left (x \right )}^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{2} \, x^{2} \log \left (x\right ) - \frac {1}{4} \, x^{2} + \frac {1}{2} \, \log \left (x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.23, size = 19, normalized size = 0.76 \begin {gather*} \frac {x^2\,\ln \left (x\right )}{2}-\frac {x^2}{4}+\frac {{\ln \left (x\right )}^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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