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

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

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integral of e^{e^x}

\int e^{e^{x}} d x

Ei (e^{x}) + C

Solution steps

\int e^{e^{x}} d x

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^{x}

= Ei (e^{x})

Add a constant to the solution

= Ei (e^{x}) + C