Optimal. Leaf size=20 \[ e^{2 e^{-2-x-x^2}} (-16+x) \]
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Rubi [A]
time = 0.03, antiderivative size = 35, normalized size of antiderivative = 1.75, number of steps
used = 1, number of rules used = 1, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {2326}
\begin {gather*} -\frac {e^{2 e^{-x^2-x-2}} \left (-2 x^2+31 x+16\right )}{2 x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^{2 e^{-2-x-x^2}} \left (16+31 x-2 x^2\right )}{1+2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.25, size = 20, normalized size = 1.00 \begin {gather*} e^{2 e^{-2-x-x^2}} (-16+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 19, normalized size = 0.95
method | result | size |
risch | \(\left (x -16\right ) {\mathrm e}^{2 \,{\mathrm e}^{-x^{2}-x -2}}\) | \(19\) |
norman | \(x \,{\mathrm e}^{2 \,{\mathrm e}^{-x^{2}-x -2}}-16 \,{\mathrm e}^{2 \,{\mathrm e}^{-x^{2}-x -2}}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 18, normalized size = 0.90 \begin {gather*} {\left (x - 16\right )} e^{\left (2 \, e^{\left (-x^{2} - x - 2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 4.52, size = 15, normalized size = 0.75 \begin {gather*} \left (x - 16\right ) e^{2 e^{- x^{2} - x - 2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 33, normalized size = 1.65 \begin {gather*} x e^{\left (2 \, e^{\left (-x^{2} - x - 2\right )}\right )} - 16 \, e^{\left (2 \, e^{\left (-x^{2} - x - 2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.10, size = 19, normalized size = 0.95 \begin {gather*} {\mathrm {e}}^{2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^{-x^2}}\,\left (x-16\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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