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

The integral from 0 to 1 of e^{e^x} is \Ei(e)-\Ei(1)

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

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

Ei (e) - Ei (1)

Solution steps

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

Apply u-substitution

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

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

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= [Ei (u)]_{1}^{e}

Compute the boundaries:

Ei (e) - Ei (1)

= Ei (e) - Ei (1)

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