What is the integral of 2x+ye^{xy} ?

The integral of 2x+ye^{xy} is x^2+e^{yx}+C

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integral of 2x+ye^{xy}

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

x^{2} + e^{y x} + C

Solution steps

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

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

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

= x^{2} + e^{y x}

Add a constant to the solution

= x^{2} + e^{y x} + C

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