Optimal. Leaf size=19 \[ e^{\frac {1}{3} (-4-x) (-2-e+3 x)} \]
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Rubi [A] time = 0.11, antiderivative size = 25, normalized size of antiderivative = 1.32, number of steps used = 3, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {12, 2244, 2236} \begin {gather*} e^{-x^2-\frac {1}{3} (10-e) x+\frac {4 (2+e)}{3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2236
Rule 2244
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{\frac {1}{3} \left (8-10 x-3 x^2+e (4+x)\right )} (-10+e-6 x) \, dx\\ &=\frac {1}{3} \int e^{\frac {4 (2+e)}{3}+\frac {1}{3} (-10+e) x-x^2} (-10+e-6 x) \, dx\\ &=e^{\frac {4 (2+e)}{3}-\frac {1}{3} (10-e) x-x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 15, normalized size = 0.79 \begin {gather*} e^{\frac {1}{3} (2+e-3 x) (4+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (-x^{2} + \frac {1}{3} \, {\left (x + 4\right )} e - \frac {10}{3} \, x + \frac {8}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 20, normalized size = 1.05 \begin {gather*} e^{\left (-x^{2} + \frac {1}{3} \, x e - \frac {10}{3} \, x + \frac {4}{3} \, e + \frac {8}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 14, normalized size = 0.74
method | result | size |
risch | \({\mathrm e}^{\frac {\left (4+x \right ) \left (-3 x +{\mathrm e}+2\right )}{3}}\) | \(14\) |
norman | \({\mathrm e}^{\frac {\left (4+x \right ) {\mathrm e}}{3}-x^{2}-\frac {10 x}{3}+\frac {8}{3}}\) | \(19\) |
gosper | \({\mathrm e}^{\frac {x \,{\mathrm e}}{3}+\frac {4 \,{\mathrm e}}{3}-x^{2}-\frac {10 x}{3}+\frac {8}{3}}\) | \(21\) |
default | \(\frac {\sqrt {\pi }\, {\mathrm e}^{\frac {4 \,{\mathrm e}}{3}+\frac {11}{3}+\frac {\left (\frac {{\mathrm e}}{3}-\frac {10}{3}\right )^{2}}{4}} \erf \left (x -\frac {{\mathrm e}}{6}+\frac {5}{3}\right )}{6}-\frac {5 \sqrt {\pi }\, {\mathrm e}^{\frac {4 \,{\mathrm e}}{3}+\frac {8}{3}+\frac {\left (\frac {{\mathrm e}}{3}-\frac {10}{3}\right )^{2}}{4}} \erf \left (x -\frac {{\mathrm e}}{6}+\frac {5}{3}\right )}{3}+{\mathrm e}^{-x^{2}+\left (\frac {{\mathrm e}}{3}-\frac {10}{3}\right ) x +\frac {4 \,{\mathrm e}}{3}+\frac {8}{3}}-\frac {\left (\frac {{\mathrm e}}{3}-\frac {10}{3}\right ) \sqrt {\pi }\, {\mathrm e}^{\frac {4 \,{\mathrm e}}{3}+\frac {8}{3}+\frac {\left (\frac {{\mathrm e}}{3}-\frac {10}{3}\right )^{2}}{4}} \erf \left (x -\frac {{\mathrm e}}{6}+\frac {5}{3}\right )}{2}\) | \(118\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (-x^{2} + \frac {1}{3} \, {\left (x + 4\right )} e - \frac {10}{3} \, x + \frac {8}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 24, normalized size = 1.26 \begin {gather*} {\mathrm {e}}^{\frac {4\,\mathrm {e}}{3}}\,{\mathrm {e}}^{-\frac {10\,x}{3}}\,{\mathrm {e}}^{8/3}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{\frac {x\,\mathrm {e}}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 22, normalized size = 1.16 \begin {gather*} e^{- x^{2} - \frac {10 x}{3} + e \left (\frac {x}{3} + \frac {4}{3}\right ) + \frac {8}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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