Optimal. Leaf size=17 \[ e^{13+e^x-x-x^2}+x \]
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Rubi [F]
time = 0.26, 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 e^{13+e^x-2 x-x^2} \left (e^{2 x}+e^{-13-e^x+2 x+x^2}+e^x (-1-2 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 \left (1+e^{13+e^x-x^2}-e^{13+e^x-x-x^2} (1+2 x)\right ) \, dx\\ &=x+\int e^{13+e^x-x^2} \, dx-\int e^{13+e^x-x-x^2} (1+2 x) \, dx\\ &=x+\int e^{13+e^x-x^2} \, dx-\int \left (e^{13+e^x-x-x^2}+2 e^{13+e^x-x-x^2} x\right ) \, dx\\ &=x-2 \int e^{13+e^x-x-x^2} x \, dx+\int e^{13+e^x-x^2} \, dx-\int e^{13+e^x-x-x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.36, size = 17, normalized size = 1.00 \begin {gather*} e^{13+e^x-x-x^2}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.31, size = 16, normalized size = 0.94
method | result | size |
risch | \(x +{\mathrm e}^{-x +{\mathrm e}^{x}-x^{2}+13}\) | \(16\) |
norman | \(\left (x \,{\mathrm e}^{-{\mathrm e}^{x}+x^{2}+2 x -13}+{\mathrm e}^{x}\right ) {\mathrm e}^{{\mathrm e}^{x}-x^{2}-2 x +13}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 15, normalized size = 0.88 \begin {gather*} x + e^{\left (-x^{2} - x + e^{x} + 13\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 15, normalized size = 0.88 \begin {gather*} x + e^{\left (-x^{2} - x + e^{x} + 13\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 17, normalized size = 1.00 \begin {gather*} x + e^{x} e^{- x^{2} - 2 x + e^{x} + 13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 20, normalized size = 1.18 \begin {gather*} {\left (x e^{x} + e^{\left (-x^{2} + e^{x} + 13\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 18, normalized size = 1.06 \begin {gather*} x+{\mathrm {e}}^{-x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{13}\,{\mathrm {e}}^{-x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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