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

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

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

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

- \frac{1}{x} + C

Solution steps

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

Cancel the common factor:

e^{- 2 x}

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