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

Optimal. Leaf size=2 \[ \text{ExpIntegralEi}(t) \]

[Out]

ExpIntegralEi[t]

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Rubi [A]  time = 0.0169777, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \text{ExpIntegralEi}(t) \]

Antiderivative was successfully verified.

[In]  Int[E^t/t,t]

[Out]

ExpIntegralEi[t]

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Rubi in Sympy [A]  time = 1.27845, size = 2, normalized size = 1. \[ \operatorname{Ei}{\left (t \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(t)/t,t)

[Out]

Ei(t)

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Mathematica [A]  time = 0.00191894, size = 2, normalized size = 1. \[ \text{ExpIntegralEi}(t) \]

Antiderivative was successfully verified.

[In]  Integrate[E^t/t,t]

[Out]

ExpIntegralEi[t]

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Maple [B]  time = 0.004, size = 8, normalized size = 4. \[ -{\it Ei} \left ( 1,-t \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(t)/t,t)

[Out]

-Ei(1,-t)

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Maxima [A]  time = 1.41408, size = 3, normalized size = 1.5 \[{\rm Ei}\left (t\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Ei(t)

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Fricas [A]  time = 0.199619, size = 3, normalized size = 1.5 \[{\rm Ei}\left (t\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Ei(t)

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Sympy [A]  time = 1.24061, size = 2, normalized size = 1. \[ \operatorname{Ei}{\left (t \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(t)/t,t)

[Out]

Ei(t)

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GIAC/XCAS [A]  time = 0.228238, size = 3, normalized size = 1.5 \[{\rm Ei}\left (t\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Ei(t)