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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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