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

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

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integral of e^{-x}x^{-2}

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

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

Solution steps

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

Simplify

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

Add a constant to the solution

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

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