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

The integral of x^2cos(y)+3y^2e^x is x^2sin(y)+e^xy^3+C

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

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

x^{2} sin (y) + e^{x} y^{3} + C

Solution steps

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

\int cos (y) x^{2} d y = x^{2} sin (y)

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

= x^{2} sin (y) + e^{x} y^{3}

Add a constant to the solution

= x^{2} sin (y) + e^{x} y^{3} + C

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