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

= \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

\frac{d}{d x} (\frac{2 x - 1}{x - 1})

\frac{\partial}{\partial x} (- x e^{- x y})

\int \frac{31 x ^{2}}{x ^{2} - 4} d x

- 1

\frac{\partial}{\partial y} (x e^{x} sin (y))