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

The integral of ((e^x))/(x^{-1)} is e^xx-e^x+C

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

integral

\frac{( e ^{x} )}{x ^{- 1}}

e^{x} x - e^{x} + C

Solution steps

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

Simplify

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

= \int e^{x} x d x

Apply Integration By Parts

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

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

= e^{x} x - e^{x}

Add a constant to the solution

= e^{x} x - e^{x} + C

What is the integral of ((e^x))/(x^{-1)} ?
The integral of ((e^x))/(x^{-1)} is e^xx-e^x+C