What is the integral from 0 to 1 of e^{e^x}e^x ?

The integral from 0 to 1 of e^{e^x}e^x is e^e-e

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integral from 0 to 1 of e^{e^x}e^x

\int_{0}^{1} e^{e^{x}} e^{x} d x

e^{e} - e

Decimal

12.43598 \dots

Solution steps

\int_{0}^{1} e^{e^{x}} e^{x} d x

Apply u-substitution

= \int_{1}^{e} e^{u} d u

Use the common integral:

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

= [e^{u}]_{1}^{e}

Compute the boundaries:

e^{e} - e

= e^{e} - e

What is the integral from 0 to 1 of e^{e^x}e^x ?
The integral from 0 to 1 of e^{e^x}e^x is e^e-e