Optimal. Leaf size=23 \[ -1+e^x-x+\frac {1}{6} x (5+\log (x)) (x+x \log (x)) \]
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Rubi [A] time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.35, number of steps used = 6, number of rules used = 4, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.160, Rules used = {12, 2194, 2304, 2305} \begin {gather*} \frac {5 x^2}{6}+\frac {1}{6} x^2 \log ^2(x)+x^2 \log (x)-x+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2304
Rule 2305
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (-3+3 e^x+8 x+7 x \log (x)+x \log ^2(x)\right ) \, dx\\ &=-x+\frac {4 x^2}{3}+\frac {1}{3} \int x \log ^2(x) \, dx+\frac {7}{3} \int x \log (x) \, dx+\int e^x \, dx\\ &=e^x-x+\frac {3 x^2}{4}+\frac {7}{6} x^2 \log (x)+\frac {1}{6} x^2 \log ^2(x)-\frac {1}{3} \int x \log (x) \, dx\\ &=e^x-x+\frac {5 x^2}{6}+x^2 \log (x)+\frac {1}{6} x^2 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 38, normalized size = 1.65 \begin {gather*} \frac {1}{3} \left (3 e^x-3 x+\frac {5 x^2}{2}+3 x^2 \log (x)+\frac {1}{2} x^2 \log ^2(x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 26, normalized size = 1.13 \begin {gather*} \frac {1}{6} \, x^{2} \log \relax (x)^{2} + x^{2} \log \relax (x) + \frac {5}{6} \, x^{2} - x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 26, normalized size = 1.13 \begin {gather*} \frac {1}{6} \, x^{2} \log \relax (x)^{2} + x^{2} \log \relax (x) + \frac {5}{6} \, x^{2} - x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 1.17
method | result | size |
default | \(-x +\frac {5 x^{2}}{6}+x^{2} \ln \relax (x )+\frac {x^{2} \ln \relax (x )^{2}}{6}+{\mathrm e}^{x}\) | \(27\) |
norman | \(-x +\frac {5 x^{2}}{6}+x^{2} \ln \relax (x )+\frac {x^{2} \ln \relax (x )^{2}}{6}+{\mathrm e}^{x}\) | \(27\) |
risch | \(-x +\frac {5 x^{2}}{6}+x^{2} \ln \relax (x )+\frac {x^{2} \ln \relax (x )^{2}}{6}+{\mathrm e}^{x}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 35, normalized size = 1.52 \begin {gather*} \frac {1}{12} \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} + \frac {7}{6} \, x^{2} \log \relax (x) + \frac {3}{4} \, x^{2} - x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.12, size = 26, normalized size = 1.13 \begin {gather*} {\mathrm {e}}^x-x+x^2\,\ln \relax (x)+\frac {x^2\,{\ln \relax (x)}^2}{6}+\frac {5\,x^2}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 27, normalized size = 1.17 \begin {gather*} \frac {x^{2} \log {\relax (x )}^{2}}{6} + x^{2} \log {\relax (x )} + \frac {5 x^{2}}{6} - x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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