What is the integral of (3x^2y+e^y) ?

The integral of (3x^2y+e^y) is e^yx+yx^3+C

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integral of (3x^2y+e^y)

\int (3 x^{2} y + e^{y}) d x

e^{y} x + y x^{3} + C

Solution steps

\int 3 x^{2} y + e^{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 e^{y} d x + \int 3 y x^{2} d x

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

\int 3 y x^{2} d x = y x^{3}

= e^{y} x + y x^{3}

Add a constant to the solution

= e^{y} x + y x^{3} + C

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What is the integral of (3x^2y+e^y) ?
The integral of (3x^2y+e^y) is e^yx+yx^3+C