Optimal. Leaf size=17 \[ -e^{-x} x+x-e^{-x} \]
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Rubi [A] time = 0.03, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.273, Rules used = {6742, 2176, 2194} \[ -e^{-x} x+x-e^{-x} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 6742
Rubi steps
\begin {align*} \int e^{-x} \left (e^x+x\right ) \, dx &=\int \left (1+e^{-x} x\right ) \, dx\\ &=x+\int e^{-x} x \, dx\\ &=x-e^{-x} x+\int e^{-x} \, dx\\ &=-e^{-x}+x-e^{-x} x\\ \end {align*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.76 \[ e^{-x} (-x-1)+x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 14, normalized size = 0.82 \[ {\left (x e^{x} - x - 1\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 11, normalized size = 0.65 \[ -{\left (x + 1\right )} e^{\left (-x\right )} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.94 \[ -x \,{\mathrm e}^{-x}+x -{\mathrm e}^{-x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 11, normalized size = 0.65 \[ -{\left (x + 1\right )} e^{\left (-x\right )} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 15, normalized size = 0.88 \[ x-{\mathrm {e}}^{-x}-x\,{\mathrm {e}}^{-x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.47 \[ x + \left (- x - 1\right ) e^{- x} \]
Verification of antiderivative is not currently implemented for this CAS.
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