Optimal. Leaf size=20 \[ \frac {1}{2} e^4 \left (5-x+\frac {\log ^2(x)}{2}\right ) \]
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Rubi [A] time = 0.08, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 6688, 2301} \begin {gather*} \frac {1}{4} e^4 \log ^2(x)-\frac {e^4 x}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2301
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} e^4 \int \frac {(-x+\log (x)) \left (10-2 x+\log ^2(x)\right )}{10 x-2 x^2+x \log ^2(x)} \, dx\\ &=\frac {1}{2} e^4 \int \left (-1+\frac {\log (x)}{x}\right ) \, dx\\ &=-\frac {e^4 x}{2}+\frac {1}{2} e^4 \int \frac {\log (x)}{x} \, dx\\ &=-\frac {e^4 x}{2}+\frac {1}{4} e^4 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} -\frac {e^4 x}{2}+\frac {1}{4} e^4 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 14, normalized size = 0.70 \begin {gather*} \frac {1}{4} \, e^{4} \log \relax (x)^{2} - \frac {1}{2} \, x e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 14, normalized size = 0.70 \begin {gather*} \frac {1}{4} \, e^{4} \log \relax (x)^{2} - \frac {1}{2} \, x e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 15, normalized size = 0.75
method | result | size |
default | \(\frac {{\mathrm e}^{4} \left (\frac {\ln \relax (x )^{2}}{2}-x \right )}{2}\) | \(15\) |
norman | \(-\frac {x \,{\mathrm e}^{4}}{2}+\frac {{\mathrm e}^{4} \ln \relax (x )^{2}}{4}\) | \(15\) |
risch | \(-\frac {x \,{\mathrm e}^{4}}{2}+\frac {{\mathrm e}^{4} \ln \relax (x )^{2}}{4}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 12, normalized size = 0.60 \begin {gather*} \frac {1}{4} \, {\left (\log \relax (x)^{2} - 2 \, x\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.28, size = 14, normalized size = 0.70 \begin {gather*} -\frac {{\mathrm {e}}^4\,\left (2\,x-{\ln \relax (x)}^2\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 15, normalized size = 0.75 \begin {gather*} - \frac {x e^{4}}{2} + \frac {e^{4} \log {\relax (x )}^{2}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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