Optimal. Leaf size=17 \[ -e^{-x} x+x-e^{-x} \]
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Rubi [A] time = 0.0313499, antiderivative size = 17, normalized size of antiderivative = 1., 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 6742
Rule 2176
Rule 2194
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*}
Mathematica [A] time = 0.0099566, size = 13, normalized size = 0.76 \[ e^{-x} (-x-1)+x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 16, normalized size = 0.9 \begin{align*} - \left ({{\rm e}^{x}} \right ) ^{-1}+x-{\frac{x}{{{\rm e}^{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.932095, size = 15, normalized size = 0.88 \begin{align*} -{\left (x + 1\right )} e^{\left (-x\right )} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.87756, size = 32, normalized size = 1.88 \begin{align*}{\left (x e^{x} - x - 1\right )} e^{\left (-x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.081333, size = 8, normalized size = 0.47 \begin{align*} x + \left (- x - 1\right ) e^{- x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.099, size = 15, normalized size = 0.88 \begin{align*} -{\left (x + 1\right )} e^{\left (-x\right )} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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