What is the integral of e^{(x+e^x)} ?

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

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integral of e^{(x+e^x)}

\int e^{(x + e^{x})} d x

e^{e^{x}} + C

Solution steps

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

Apply u-substitution

= \int e^{u} d u

Use the common integral:

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

= e^{u}

Substitute back

u = e^{x}

= e^{e^{x}}

Add a constant to the solution

= e^{e^{x}} + C