What is the integral of (e^{-2x})/((xe^{-x))^2} ?

The integral of (e^{-2x})/((xe^{-x))^2} is -1/x+C

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integral of (e^{-2x})/((xe^{-x))^2}

\int \frac{e ^{- 2 x}}{( x e ^{- x} ) ^{2}} d x

- \frac{1}{x} + C

Solution steps

\int \frac{e ^{- 2 x}}{( x e ^{- x} ) ^{2}} d x

Simplify

\frac{e ^{- 2 x}}{( x e ^{- x} ) ^{2}} : \frac{1}{x ^{2}}

= \int \frac{1}{x ^{2}} d x

Apply the Power Rule

: - \frac{1}{x}

= - \frac{1}{x}

Add a constant to the solution

= - \frac{1}{x} + C

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What is the integral of (e^{-2x})/((xe^{-x))^2} ?
The integral of (e^{-2x})/((xe^{-x))^2} is -1/x+C