What is the integral from 0 to x of (e^{-x})/x ?

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

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integral from 0 to x of (e^{-x})/x

\int_{0}^{x} \frac{e ^{- x}}{x} d x

Ei (- x) - Ei (0)

Solution steps

\int_{0}^{x} \frac{e ^{- x}}{x} d x

Apply u-substitution

: \int_{0}^{- x} \frac{e ^{u}}{u} d u

= \int_{0}^{- x} \frac{e ^{u}}{u} d u

Use the nonelementary integral:

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

= [Ei (u)]_{0}^{- x}

Compute the boundaries:

Ei (- x) - Ei (0)

= Ei (- x) - Ei (0)

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