What is the integral of (e^{-5x})/x ?

The integral of (e^{-5x})/x is \Ei(-5x)+C

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integral of (e^{-5x})/x

\int \frac{e ^{- 5 x}}{x} d x

Ei (- 5 x) + C

Solution steps

\int \frac{e ^{- 5 x}}{x} d x

Apply u-substitution

: \int \frac{e ^{u}}{u} d u

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

Use the nonelementary integral:

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

= Ei (u)

Substitute back

u = - 5 x

= Ei (- 5 x)

Add a constant to the solution

= Ei (- 5 x) + C

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