What is the integral of (e^y)/(x^2) ?

The integral of (e^y)/(x^2) is -(e^y)/x+C

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integral of (e^y)/(x^2)

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

- \frac{e ^{y}}{x} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{y} \cdot \int \frac{1}{x ^{2}} d x

Apply the Power Rule

: - \frac{1}{x}

= e^{y} (- \frac{1}{x})

Simplify

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

= - \frac{e ^{y}}{x}

Add a constant to the solution

= - \frac{e ^{y}}{x} + C

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