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

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

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integral from 0 to 1 of e^te^{e^t}

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

e^{e} - e

Decimal

12.43598 \dots

Solution steps

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

Apply u-substitution

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

= \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

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