Optimal. Leaf size=16 \[ -e^{-t} t-e^{-t} \]
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Rubi [A] time = 0.0086793, antiderivative size = 16, normalized size of antiderivative = 1., 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} \[ -e^{-t} t-e^{-t} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{-t} t \, dt &=-e^{-t} t+\int e^{-t} \, dt\\ &=-e^{-t}-e^{-t} t\\ \end{align*}
Mathematica [A] time = 0.0043066, size = 11, normalized size = 0.69 \[ e^{-t} (-t-1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 10, normalized size = 0.6 \begin{align*} -{\frac{1+t}{{{\rm e}^{t}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.924738, size = 12, normalized size = 0.75 \begin{align*} -{\left (t + 1\right )} e^{\left (-t\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.9907, size = 23, normalized size = 1.44 \begin{align*} -{\left (t + 1\right )} e^{\left (-t\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.073225, size = 7, normalized size = 0.44 \begin{align*} \left (- t - 1\right ) e^{- t} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04802, size = 12, normalized size = 0.75 \begin{align*} -{\left (t + 1\right )} e^{\left (-t\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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