3.173 \(\int \frac{e^{2 t}}{-1+t} \, dt\)

Optimal. Leaf size=12 \[ e^2 \text{ExpIntegralEi}(-2 (1-t)) \]

[Out]

E^2*ExpIntegralEi[-2*(1 - t)]

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Rubi [A]  time = 0.0269893, 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 \[ e^2 \text{ExpIntegralEi}(-2 (1-t)) \]

Antiderivative was successfully verified.

[In]  Int[E^(2*t)/(-1 + t),t]

[Out]

E^2*ExpIntegralEi[-2*(1 - t)]

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Rubi in Sympy [A]  time = 1.59817, size = 8, normalized size = 0.67 \[ e^{2} \operatorname{Ei}{\left (2 t - 2 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(2*t)/(-1+t),t)

[Out]

exp(2)*Ei(2*t - 2)

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Mathematica [A]  time = 0.00358669, size = 10, normalized size = 0.83 \[ e^2 \text{ExpIntegralEi}(2 (t-1)) \]

Antiderivative was successfully verified.

[In]  Integrate[E^(2*t)/(-1 + t),t]

[Out]

E^2*ExpIntegralEi[2*(-1 + t)]

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Maple [A]  time = 0.006, size = 12, normalized size = 1. \[ -{{\rm e}^{2}}{\it Ei} \left ( 1,-2\,t+2 \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(2*t)/(-1+t),t)

[Out]

-exp(2)*Ei(1,-2*t+2)

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Maxima [A]  time = 1.43033, size = 15, normalized size = 1.25 \[ -e^{2} exp_integral_e\left (1, -2 \, t + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(2*t)/(t - 1),t, algorithm="maxima")

[Out]

-e^2*exp_integral_e(1, -2*t + 2)

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Fricas [A]  time = 0.199384, size = 12, normalized size = 1. \[{\rm Ei}\left (2 \, t - 2\right ) e^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(2*t)/(t - 1),t, algorithm="fricas")

[Out]

Ei(2*t - 2)*e^2

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{2 t}}{t - 1}\, dt \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(2*t)/(-1+t),t)

[Out]

Integral(exp(2*t)/(t - 1), t)

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GIAC/XCAS [A]  time = 0.224413, size = 12, normalized size = 1. \[{\rm Ei}\left (2 \, t - 2\right ) e^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(2*t)/(t - 1),t, algorithm="giac")

[Out]

Ei(2*t - 2)*e^2