Optimal. Leaf size=18 \[ e^{1+2 x-e^{-x} x (1+x)} \]
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Rubi [F] time = 0.64, 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^{-x+e^{-x} \left (-x-x^2+e^x (1+2 x)\right )} \left (-1+2 e^x-x+x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{e^{-x} \left (e^x-x\right ) (1+x)} \left (-1+2 e^x-x+x^2\right ) \, dx\\ &=\int \left (-e^{e^{-x} \left (e^x-x\right ) (1+x)}+2 e^{x+e^{-x} \left (e^x-x\right ) (1+x)}-e^{e^{-x} \left (e^x-x\right ) (1+x)} x+e^{e^{-x} \left (e^x-x\right ) (1+x)} x^2\right ) \, dx\\ &=2 \int e^{x+e^{-x} \left (e^x-x\right ) (1+x)} \, dx-\int e^{e^{-x} \left (e^x-x\right ) (1+x)} \, dx-\int e^{e^{-x} \left (e^x-x\right ) (1+x)} x \, dx+\int e^{e^{-x} \left (e^x-x\right ) (1+x)} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.21, size = 18, normalized size = 1.00 \begin {gather*} e^{1+2 x-e^{-x} x (1+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 21, normalized size = 1.17 \begin {gather*} e^{\left (-{\left (x^{2} - {\left (x + 1\right )} e^{x} + x\right )} e^{\left (-x\right )} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.41, size = 22, normalized size = 1.22 \begin {gather*} e^{\left (-x^{2} e^{\left (-x\right )} - x e^{\left (-x\right )} + 2 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 23, normalized size = 1.28
method | result | size |
risch | \({\mathrm e}^{\left (2 \,{\mathrm e}^{x} x -x^{2}+{\mathrm e}^{x}-x \right ) {\mathrm e}^{-x}}\) | \(23\) |
norman | \({\mathrm e}^{\left (\left (2 x +1\right ) {\mathrm e}^{x}-x^{2}-x \right ) {\mathrm e}^{-x}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 22, normalized size = 1.22 \begin {gather*} e^{\left (-x^{2} e^{\left (-x\right )} - x e^{\left (-x\right )} + 2 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.66, size = 25, normalized size = 1.39 \begin {gather*} {\mathrm {e}}^{2\,x}\,\mathrm {e}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^{-x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 17, normalized size = 0.94 \begin {gather*} e^{\left (- x^{2} - x + \left (2 x + 1\right ) e^{x}\right ) e^{- x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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