3.161 \(\int e^{\frac{1}{t}} \, dt\)

Optimal. Leaf size=14 \[ e^{\frac{1}{t}} t-\text{ExpIntegralEi}\left (\frac{1}{t}\right ) \]

[Out]

E^t^(-1)*t - ExpIntegralEi[t^(-1)]

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Rubi [A]  time = 0.0225486, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4 \[ e^{\frac{1}{t}} t-\text{ExpIntegralEi}\left (\frac{1}{t}\right ) \]

Antiderivative was successfully verified.

[In]  Int[E^t^(-1),t]

[Out]

E^t^(-1)*t - ExpIntegralEi[t^(-1)]

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Rubi in Sympy [A]  time = 1.36337, size = 10, normalized size = 0.71 \[ t e^{\frac{1}{t}} - \operatorname{Ei}{\left (\frac{1}{t} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(1/t),t)

[Out]

t*exp(1/t) - Ei(1/t)

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Mathematica [A]  time = 0.00308048, size = 14, normalized size = 1. \[ e^{\frac{1}{t}} t-\text{ExpIntegralEi}\left (\frac{1}{t}\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[E^t^(-1),t]

[Out]

E^t^(-1)*t - ExpIntegralEi[t^(-1)]

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Maple [A]  time = 0.004, size = 15, normalized size = 1.1 \[{{\rm e}^{{t}^{-1}}}t+{\it Ei} \left ( 1,-{t}^{-1} \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(1/t),t)

[Out]

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

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Maxima [A]  time = 1.40561, size = 18, normalized size = 1.29 \[ t e^{\frac{1}{t}} -{\rm Ei}\left (\frac{1}{t}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

t*e^(1/t) - Ei(1/t)

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Fricas [A]  time = 0.202327, size = 18, normalized size = 1.29 \[ t e^{\frac{1}{t}} -{\rm Ei}\left (\frac{1}{t}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

t*e^(1/t) - Ei(1/t)

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Sympy [A]  time = 1.70326, size = 10, normalized size = 0.71 \[ t e^{\frac{1}{t}} - \operatorname{Ei}{\left (\frac{1}{t} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(1/t),t)

[Out]

t*exp(1/t) - Ei(1/t)

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \mathit{undef} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

undef