Optimal. Leaf size=15 \[ e^{-a-1} \text{ExpIntegralEi}(a-t+1) \]
[Out]
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Rubi [A] time = 0.0338097, 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 \[ e^{-a-1} \text{ExpIntegralEi}(a-t+1) \]
Antiderivative was successfully verified.
[In] Int[1/(E^t*(-1 - a + t)),t]
[Out]
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Rubi in Sympy [A] time = 2.02819, size = 12, normalized size = 0.8 \[ e^{- a - 1} \operatorname{Ei}{\left (a - t + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/exp(t)/(-1-a+t),t)
[Out]
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Mathematica [A] time = 0.00724314, size = 15, normalized size = 1. \[ e^{-a-1} \text{ExpIntegralEi}(a-t+1) \]
Antiderivative was successfully verified.
[In] Integrate[1/(E^t*(-1 - a + t)),t]
[Out]
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Maple [A] time = 0.023, size = 17, normalized size = 1.1 \[ -{{\rm e}^{-1-a}}{\it Ei} \left ( 1,-1-a+t \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/exp(t)/(-1-a+t),t)
[Out]
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Maxima [A] time = 1.44247, size = 22, normalized size = 1.47 \[ -e^{\left (-a - 1\right )} exp_integral_e\left (1, -a + t - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-e^(-t)/(a - t + 1),t, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199377, size = 19, normalized size = 1.27 \[{\rm Ei}\left (a - t + 1\right ) e^{\left (-a - 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-e^(-t)/(a - t + 1),t, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{- t}}{- a + t - 1}\, dt \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/exp(t)/(-1-a+t),t)
[Out]
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GIAC/XCAS [A] time = 0.232198, size = 19, normalized size = 1.27 \[{\rm Ei}\left (a - t + 1\right ) e^{\left (-a - 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-e^(-t)/(a - t + 1),t, algorithm="giac")
[Out]