What is the integral of e^{e^t} ?

The integral of e^{e^t} is \Ei(e^t)+C

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integral of e^{e^t}

\int e^{e^{t}} d t

Ei (e^{t}) + C

Solution steps

\int e^{e^{t}} d t

Apply u-substitution

= \int \frac{e ^{u}}{u} d u

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= Ei (u)

Substitute back

u = e^{t}

= Ei (e^{t})

Add a constant to the solution

= Ei (e^{t}) + C

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