What is the integral of (ye^{xy}+y/(x^2)) ?

The integral of (ye^{xy}+y/(x^2)) is -y/x+e^{yx}+C

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integral of (ye^{xy}+y/(x^2))

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

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

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{y}{x ^{2}} d x = - \frac{y}{x}

\int y e^{y x} d x = e^{y x}

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

Add a constant to the solution

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

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What is the integral of (ye^{xy}+y/(x^2)) ?
The integral of (ye^{xy}+y/(x^2)) is -y/x+e^{yx}+C