Optimal. Leaf size=20 \[ 4 e^{-3+e^x-x+e^{-x} x} x \]
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Rubi [F] time = 0.98, 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 \exp \left (-x+e^{-x} \left (e^{2 x}+e^x (-3-x)+x-e^x \log (x)+e^x \log (4 x)\right )\right ) \left (e^x (1-x)+x+e^{2 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 4 e^{-3+e^x-2 x+e^{-x} x} \left (e^x+x-e^x x+e^{2 x} x-x^2\right ) \, dx\\ &=4 \int e^{-3+e^x-2 x+e^{-x} x} \left (e^x+x-e^x x+e^{2 x} x-x^2\right ) \, dx\\ &=4 \int \left (e^{-3+e^x-x+e^{-x} x}+e^{-3+e^x+e^{-x} x} x+e^{-3+e^x-2 x+e^{-x} x} x-e^{-3+e^x-x+e^{-x} x} x-e^{-3+e^x-2 x+e^{-x} x} x^2\right ) \, dx\\ &=4 \int e^{-3+e^x-x+e^{-x} x} \, dx+4 \int e^{-3+e^x+e^{-x} x} x \, dx+4 \int e^{-3+e^x-2 x+e^{-x} x} x \, dx-4 \int e^{-3+e^x-x+e^{-x} x} x \, dx-4 \int e^{-3+e^x-2 x+e^{-x} x} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.61, size = 20, normalized size = 1.00 \begin {gather*} 4 e^{-3+e^x-x+e^{-x} x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 33, normalized size = 1.65 \begin {gather*} x e^{\left (-{\left ({\left (2 \, x - 2 \, \log \relax (2) + 3\right )} e^{x} - x - e^{\left (2 \, x\right )}\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 = 2.18, size = 20, normalized size = 1.00 \begin {gather*} 4 \, x e^{\left ({\left (x + e^{\left (2 \, x\right )}\right )} e^{\left (-x\right )} - x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.23, size = 30, normalized size = 1.50
method | result | size |
risch | \(x \,{\mathrm e}^{\left (2 \,{\mathrm e}^{x} \ln \relax (2)-{\mathrm e}^{x} x -3 \,{\mathrm e}^{x}+{\mathrm e}^{2 x}+x \right ) {\mathrm e}^{-x}}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 17, normalized size = 0.85 \begin {gather*} 4 \, x e^{\left (x e^{\left (-x\right )} - x + e^{x} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int {\mathrm {e}}^{-x}\,{\mathrm {e}}^{{\mathrm {e}}^{-x}\,\left (x+{\mathrm {e}}^{2\,x}-{\mathrm {e}}^x\,\left (x+3\right )-{\mathrm {e}}^x\,\ln \relax (x)+\ln \left (4\,x\right )\,{\mathrm {e}}^x\right )}\,\left (x+x\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^x\,\left (x-1\right )-x^2\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.43, size = 37, normalized size = 1.85 \begin {gather*} x e^{\left (x + \left (- x - 3\right ) e^{x} + \left (\log {\relax (x )} + \log {\relax (4 )}\right ) e^{x} + e^{2 x} - e^{x} \log {\relax (x )}\right ) e^{- x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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