What is the integral of xcos(y)+cos(z) ?

The integral of xcos(y)+cos(z) is cos(z)y+xsin(y)+C

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integral of xcos(y)+cos(z)

\int x cos (y) + cos (z) d y

cos (z) y + x sin (y) + C

Solution steps

\int x cos (y) + cos (z) 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 (z) d y + \int cos (y) x d y

\int cos (z) d y = cos (z) y

\int cos (y) x d y = x sin (y)

= cos (z) y + x sin (y)

Add a constant to the solution

= cos (z) y + x sin (y) + C

What is the integral of xcos(y)+cos(z) ?
The integral of xcos(y)+cos(z) is cos(z)y+xsin(y)+C