Optimal. Leaf size=19 \[ e^5-4 e^{-2+e^x-x} x^2 \]
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Rubi [A]
time = 0.03, antiderivative size = 33, normalized size of antiderivative = 1.74, number of steps
used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {2326}
\begin {gather*} -\frac {4 e^{-x+e^x-2} \left (x^2-e^x x^2\right )}{1-e^x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {4 e^{-2+e^x-x} \left (x^2-e^x x^2\right )}{1-e^x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 0.79 \begin {gather*} -4 e^{-2+e^x-x} x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 14, normalized size = 0.74
method | result | size |
risch | \(-4 x^{2} {\mathrm e}^{{\mathrm e}^{x}-2-x}\) | \(14\) |
norman | \(-4 \,{\mathrm e}^{-2} x^{2} {\mathrm e}^{{\mathrm e}^{x}-x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 13, normalized size = 0.68 \begin {gather*} -4 \, x^{2} e^{\left (-x + e^{x} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 13, normalized size = 0.68 \begin {gather*} -4 \, x^{2} e^{\left (-x + e^{x} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 15, normalized size = 0.79 \begin {gather*} - \frac {4 x^{2} e^{- x + e^{x}}}{e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 13, normalized size = 0.68 \begin {gather*} -4 \, x^{2} e^{\left (-x + e^{x} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.14, size = 14, normalized size = 0.74 \begin {gather*} -4\,x^2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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