Optimal. Leaf size=16 \[ -e^{-x} x-e^{-x} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {2176, 2194} \[ -e^{-x} x-e^{-x} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {align*} \int e^{-x} x \, dx &=-e^{-x} x+\int e^{-x} \, dx\\ &=-e^{-x}-e^{-x} x\\ \end {align*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 0.69 \[ e^{-x} (-x-1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 9, normalized size = 0.56 \[ -{\left (x + 1\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.02, size = 9, normalized size = 0.56 \[ -{\left (x + 1\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.62 \[ -\left (x +1\right ) {\mathrm e}^{-x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 9, normalized size = 0.56 \[ -{\left (x + 1\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 9, normalized size = 0.56 \[ -{\mathrm {e}}^{-x}\,\left (x+1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 7, normalized size = 0.44 \[ \left (- x - 1\right ) e^{- x} \]
Verification of antiderivative is not currently implemented for this CAS.
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