Optimal. Leaf size=24 \[ 2 e^{-3 \left (4-(e+x) \left (x-\frac {\log (x)}{5}\right )\right )} x^2 \]
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Rubi [B] time = 0.09, antiderivative size = 71, normalized size of antiderivative = 2.96, number of steps used = 2, number of rules used = 2, integrand size = 64, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {12, 2288} \begin {gather*} -\frac {2 e^{-3 \left (-x^2-e x+4\right )} x^{-\frac {3}{5} (x+e)} \left (-10 x^3+x^2+e \left (x-5 x^2\right )+x^2 \log (x)\right )}{10 x-\frac {x+e}{x}-\log (x)+5 e} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \exp \left (\frac {1}{5} \left (-60+15 e x+15 x^2-(3 e+3 x) \log (x)\right )\right ) \left (20 x-6 x^2+60 x^3+e \left (-6 x+30 x^2\right )-6 x^2 \log (x)\right ) \, dx\\ &=-\frac {2 e^{-3 \left (4-e x-x^2\right )} x^{-\frac {3}{5} (e+x)} \left (x^2-10 x^3+e \left (x-5 x^2\right )+x^2 \log (x)\right )}{5 e+10 x-\frac {e+x}{x}-\log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.99, size = 26, normalized size = 1.08 \begin {gather*} 2 e^{-12+3 e x+3 x^2} x^{2-\frac {3 (e+x)}{5}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 26, normalized size = 1.08 \begin {gather*} 2 \, x^{2} e^{\left (3 \, x^{2} + 3 \, x e - \frac {3}{5} \, {\left (x + e\right )} \log \relax (x) - 12\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 29, normalized size = 1.21 \begin {gather*} 2 \, x^{2} e^{\left (3 \, x^{2} + 3 \, x e - \frac {3}{5} \, x \log \relax (x) - \frac {3}{5} \, e \log \relax (x) - 12\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 31, normalized size = 1.29
method | result | size |
risch | \(2 x^{2} x^{-\frac {3 x}{5}-\frac {3 \,{\mathrm e}}{5}} {\mathrm e}^{-12+3 x \,{\mathrm e}+3 x^{2}}\) | \(31\) |
norman | \(2 x^{2} {\mathrm e}^{\left (3 \,{\mathrm e}+3 x \right ) \ln \left (\frac {1}{x^{\frac {1}{5}}}\right )+3 x \,{\mathrm e}+3 x^{2}-12}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 29, normalized size = 1.21 \begin {gather*} 2 \, x^{2} e^{\left (3 \, x^{2} + 3 \, x e - \frac {3}{5} \, x \log \relax (x) - \frac {3}{5} \, e \log \relax (x) - 12\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.30, size = 27, normalized size = 1.12 \begin {gather*} 2\,x^{2-\frac {3\,\mathrm {e}}{5}-\frac {3\,x}{5}}\,{\mathrm {e}}^{-12}\,{\mathrm {e}}^{3\,x^2}\,{\mathrm {e}}^{3\,x\,\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 34, normalized size = 1.42 \begin {gather*} 2 x^{2} e^{3 x^{2} + 3 e x - \left (\frac {3 x}{5} + \frac {3 e}{5}\right ) \log {\relax (x )} - 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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