3.159 \(\int \frac{e^{a t}}{t} \, dt\)

Optimal. Leaf size=4 \[ \text{ExpIntegralEi}(a t) \]

[Out]

ExpIntegralEi[a*t]

_______________________________________________________________________________________

Rubi [A]  time = 0.0208139, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \text{ExpIntegralEi}(a t) \]

Antiderivative was successfully verified.

[In]  Int[E^(a*t)/t,t]

[Out]

ExpIntegralEi[a*t]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.36631, size = 3, normalized size = 0.75 \[ \operatorname{Ei}{\left (a t \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(a*t)/t,t)

[Out]

Ei(a*t)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00196054, size = 4, normalized size = 1. \[ \text{ExpIntegralEi}(a t) \]

Antiderivative was successfully verified.

[In]  Integrate[E^(a*t)/t,t]

[Out]

ExpIntegralEi[a*t]

_______________________________________________________________________________________

Maple [A]  time = 0.004, size = 9, normalized size = 2.3 \[ -{\it Ei} \left ( 1,-at \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(a*t)/t,t)

[Out]

-Ei(1,-a*t)

_______________________________________________________________________________________

Maxima [A]  time = 1.41595, size = 5, normalized size = 1.25 \[{\rm Ei}\left (a t\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Ei(a*t)

_______________________________________________________________________________________

Fricas [A]  time = 0.198334, size = 5, normalized size = 1.25 \[{\rm Ei}\left (a t\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Ei(a*t)

_______________________________________________________________________________________

Sympy [A]  time = 1.34288, size = 3, normalized size = 0.75 \[ \operatorname{Ei}{\left (a t \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(a*t)/t,t)

[Out]

Ei(a*t)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.210192, size = 5, normalized size = 1.25 \[{\rm Ei}\left (a t\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Ei(a*t)