3.160 \(\int \frac{e^t}{t^2} \, dt\)

Optimal. Leaf size=11 \[ \text{ExpIntegralEi}(t)-\frac{e^t}{t} \]

[Out]

-(E^t/t) + ExpIntegralEi[t]

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Rubi [A]  time = 0.0333979, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \text{ExpIntegralEi}(t)-\frac{e^t}{t} \]

Antiderivative was successfully verified.

[In]  Int[E^t/t^2,t]

[Out]

-(E^t/t) + ExpIntegralEi[t]

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Rubi in Sympy [A]  time = 1.89631, size = 7, normalized size = 0.64 \[ \operatorname{Ei}{\left (t \right )} - \frac{e^{t}}{t} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(t)/t**2,t)

[Out]

Ei(t) - exp(t)/t

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Mathematica [A]  time = 0.0048487, size = 11, normalized size = 1. \[ \text{ExpIntegralEi}(t)-\frac{e^t}{t} \]

Antiderivative was successfully verified.

[In]  Integrate[E^t/t^2,t]

[Out]

-(E^t/t) + ExpIntegralEi[t]

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Maple [A]  time = 0.004, size = 16, normalized size = 1.5 \[ -{\frac{{{\rm e}^{t}}}{t}}-{\it Ei} \left ( 1,-t \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(t)/t^2,t)

[Out]

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

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Maxima [A]  time = 1.42966, size = 7, normalized size = 0.64 \[ \Gamma \left (-1, -t\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

gamma(-1, -t)

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Fricas [A]  time = 0.197507, size = 18, normalized size = 1.64 \[ \frac{t{\rm Ei}\left (t\right ) - e^{t}}{t} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(t*Ei(t) - e^t)/t

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Sympy [A]  time = 1.60351, size = 7, normalized size = 0.64 \[ \operatorname{Ei}{\left (t \right )} - \frac{e^{t}}{t} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(t)/t**2,t)

[Out]

Ei(t) - exp(t)/t

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GIAC/XCAS [A]  time = 0.226251, size = 18, normalized size = 1.64 \[ \frac{t{\rm Ei}\left (t\right ) - e^{t}}{t} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(t*Ei(t) - e^t)/t