Optimal. Leaf size=12 \[ e^2 \text{ExpIntegralEi}(-2 (1-t)) \]
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Rubi [A] time = 0.0148496, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {2178} \[ e^2 \text{ExpIntegralEi}(-2 (1-t)) \]
Antiderivative was successfully verified.
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Rule 2178
Rubi steps
\begin{align*} \int \frac{e^{2 t}}{-1+t} \, dt &=e^2 \text{Ei}(-2 (1-t))\\ \end{align*}
Mathematica [A] time = 0.0131442, size = 10, normalized size = 0.83 \[ e^2 \text{ExpIntegralEi}(2 (t-1)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, normalized size = 1. \begin{align*} -{{\rm e}^{2}}{\it Ei} \left ( 1,-2\,t+2 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03601, size = 15, normalized size = 1.25 \begin{align*} -e^{2} E_{1}\left (-2 \, t + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.12668, size = 23, normalized size = 1.92 \begin{align*}{\rm Ei}\left (2 \, t - 2\right ) e^{2} \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^{2 t}}{t - 1}\, dt \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08619, size = 12, normalized size = 1. \begin{align*}{\rm Ei}\left (2 \, t - 2\right ) e^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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