Optimal. Leaf size=12 \[ e^2 \text {Ei}(-2 (1-t)) \]
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Rubi [A]
time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, 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 = {2209}
\begin {gather*} e^2 \text {ExpIntegralEi}(-2 (1-t)) \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {align*} \int \frac {e^{2 t}}{-1+t} \, dt &=e^2 \text {Ei}(-2 (1-t))\\ \end {align*}
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Mathematica [A]
time = 0.04, size = 10, normalized size = 0.83 \begin {gather*} e^2 \text {Ei}(2 (-1+t)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 12, normalized size = 1.00
method | result | size |
derivativedivides | \(-{\mathrm e}^{2} \expIntegral \left (1, -2 t +2\right )\) | \(12\) |
default | \(-{\mathrm e}^{2} \expIntegral \left (1, -2 t +2\right )\) | \(12\) |
risch | \(-{\mathrm e}^{2} \expIntegral \left (1, -2 t +2\right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.10, size = 11, normalized size = 0.92 \begin {gather*} -e^{2} E_{1}\left (-2 \, t + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.86, size = 9, normalized size = 0.75 \begin {gather*} {\rm Ei}\left (2 \, t - 2\right ) e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{2 t}}{t - 1}\, dt \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.48, size = 9, normalized size = 0.75 \begin {gather*} {\rm Ei}\left (2 \, t - 2\right ) e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 9, normalized size = 0.75 \begin {gather*} {\mathrm {e}}^2\,\mathrm {ei}\left (2\,t-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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