Optimal. Leaf size=15 \[ e^{-a-1} \text{ExpIntegralEi}(a-t+1) \]
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Rubi [A] time = 0.0153825, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {2178} \[ e^{-a-1} \text{ExpIntegralEi}(a-t+1) \]
Antiderivative was successfully verified.
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Rule 2178
Rubi steps
\begin{align*} \int \frac{e^{-t}}{-1-a+t} \, dt &=e^{-1-a} \text{Ei}(1+a-t)\\ \end{align*}
Mathematica [A] time = 0.0117154, size = 15, normalized size = 1. \[ e^{-a-1} \text{ExpIntegralEi}(a-t+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 17, normalized size = 1.1 \begin{align*} -{{\rm e}^{-1-a}}{\it Ei} \left ( 1,-1-a+t \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03949, size = 22, normalized size = 1.47 \begin{align*} -e^{\left (-a - 1\right )} E_{1}\left (-a + t - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.1479, size = 35, normalized size = 2.33 \begin{align*}{\rm Ei}\left (a - t + 1\right ) e^{\left (-a - 1\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{- t}}{- a + t - 1}\, dt \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08339, size = 19, normalized size = 1.27 \begin{align*}{\rm Ei}\left (a - t + 1\right ) e^{\left (-a - 1\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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