What is the integral of x^{-2}e^x ?

The integral of x^{-2}e^x is -(e^x)/x+\Ei(x)+C

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integral of x^{-2}e^x

\int x^{- 2} e^{x} d x

- \frac{e ^{x}}{x} + Ei (x) + C

Solution steps

\int x^{- 2} e^{x} d x

Simplify

x^{- 2} e^{x} : \frac{e ^{x}}{x ^{2}}

= \int \frac{e ^{x}}{x ^{2}} d x

Apply Integration By Parts

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

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

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

= - \frac{e ^{x}}{x} - (- Ei (x))

Simplify

= - \frac{e ^{x}}{x} + Ei (x)

Add a constant to the solution

= - \frac{e ^{x}}{x} + Ei (x) + C

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What is the integral of x^{-2}e^x ?
The integral of x^{-2}e^x is -(e^x)/x+\Ei(x)+C