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)

Add a constant to the solution

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

y^{^{''}} + 10 y^{^{'}} + 34 y = 0

x d y - y d x = 2 x^{2} y^{2} d y, y (1) = 2

\frac{d}{d x} (cos (2 x) cos (x))

\int \frac{8 - 3 x}{25 - 64 x ^{2}} d x

(x - 3) (x^{2} + 6)

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