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

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