What is the integral of 2y+xe^{xy} ?

The integral of 2y+xe^{xy} is y^2+e^{xy}+C

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integral of 2y+xe^{xy}

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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