What is the integral of (xz-e^xsin(y)) ?

The integral of (xz-e^xsin(y)) is e^xcos(y)+xzy+C

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integral of (xz-e^xsin(y))

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

e^{x} cos (y) + x zy + C

Solution steps

\int x z - e^{x} sin (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 sin (y) e^{x} d y + \int x z d y

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

\int x z d y = x zy

= - (- e^{x} cos (y)) + x zy

Simplify

= e^{x} cos (y) + x zy

Add a constant to the solution

= e^{x} cos (y) + x zy + C

What is the integral of (xz-e^xsin(y)) ?
The integral of (xz-e^xsin(y)) is e^xcos(y)+xzy+C