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

The integral of e^x*e^{e^x} is e^{e^x}+C

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integral of e^x*e^{e^x}

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

e^{e^{x}} + C

Solution steps

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

Apply u-substitution

: \int e^{u} d u

= \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

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