Optimal. Leaf size=14 \[ 2 e^2 \left (3-x^{-2+x}\right ) \]
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Rubi [F] time = 0.13, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int x^{-3+x} \left (e^2 (4-2 x)-2 e^2 x \log (x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 2 e^2 x^{-3+x} (2-x-x \log (x)) \, dx\\ &=\left (2 e^2\right ) \int x^{-3+x} (2-x-x \log (x)) \, dx\\ &=\left (2 e^2\right ) \int \left (2 x^{-3+x}-x^{-2+x}-x^{-2+x} \log (x)\right ) \, dx\\ &=-\left (\left (2 e^2\right ) \int x^{-2+x} \, dx\right )-\left (2 e^2\right ) \int x^{-2+x} \log (x) \, dx+\left (4 e^2\right ) \int x^{-3+x} \, dx\\ &=-\left (\left (2 e^2\right ) \int x^{-2+x} \, dx\right )+\left (2 e^2\right ) \int \frac {\int x^{-2+x} \, dx}{x} \, dx+\left (4 e^2\right ) \int x^{-3+x} \, dx-\left (2 e^2 \log (x)\right ) \int x^{-2+x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 10, normalized size = 0.71 \begin {gather*} -2 e^2 x^{-2+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 9, normalized size = 0.64 \begin {gather*} -2 \, x^{x - 2} e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 9, normalized size = 0.64 \begin {gather*} -2 \, x^{x - 2} e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 10, normalized size = 0.71
method | result | size |
risch | \(-2 \,{\mathrm e}^{2} x^{x -2}\) | \(10\) |
norman | \(-2 \,{\mathrm e}^{2} {\mathrm e}^{\left (x -2\right ) \ln \relax (x )}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 12, normalized size = 0.86 \begin {gather*} -\frac {2 \, e^{\left (x \log \relax (x) + 2\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.05, size = 9, normalized size = 0.64 \begin {gather*} -2\,x^{x-2}\,{\mathrm {e}}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 14, normalized size = 1.00 \begin {gather*} - 2 e^{2} e^{\left (x - 2\right ) \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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