What is the integral of e^x(x)^{-1} ?

The integral of e^x(x)^{-1} is \Ei(x)+C

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integral of e^x(x)^{-1}

\int e^{x} (x)^{- 1} d x

Ei (x) + C

Solution steps

\int e^{x} x^{- 1} d x

Simplify

e^{x} x^{- 1} : \frac{e ^{x}}{x}

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

Use the nonelementary integral:

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

= Ei (x)

Add a constant to the solution

= Ei (x) + C