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 = 0.009748, 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, Rules used = {2178} \[ \text{ExpIntegralEi}(t) \]

Antiderivative was successfully verified.

[In]

Int[E^t/t,t]

[Out]

ExpIntegralEi[t]

Rule 2178

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral
Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !$UseGamma === True

Rubi steps

\begin{align*} \int \frac{e^t}{t} \, dt &=\text{Ei}(t)\\ \end{align*}

Mathematica [A]  time = 0.0049735, 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 = 0.002, size = 8, normalized size = 4. \begin{align*} -{\it Ei} \left ( 1,-t \right ) \end{align*}

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 = 1.03039, size = 3, normalized size = 1.5 \begin{align*}{\rm Ei}\left (t\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(t)/t,t, algorithm="maxima")

[Out]

Ei(t)

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Fricas [A]  time = 1.09348, size = 9, normalized size = 4.5 \begin{align*}{\rm Ei}\left (t\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(t)/t,t, algorithm="fricas")

[Out]

Ei(t)

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Sympy [A]  time = 0.732115, size = 2, normalized size = 1. \begin{align*} \operatorname{Ei}{\left (t \right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(t)/t,t)

[Out]

Ei(t)

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Giac [A]  time = 1.10123, size = 3, normalized size = 1.5 \begin{align*}{\rm Ei}\left (t\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(t)/t,t, algorithm="giac")

[Out]

Ei(t)