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

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

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integral of x^{-1}e^x

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

Ei (x) + C

Solution steps

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

Simplify

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

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