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

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

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integral of e^y+x^2e^{xy}

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

What is the integral of e^y+x^2e^{xy} ?
The integral of e^y+x^2e^{xy} is e^y+xe^{xy}+C