What is the integral of xcos(xz)+xy ?

The integral of xcos(xz)+xy is sin(xz)+xyz+C

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integral of xcos(xz)+xy

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

sin (x z) + x yz + C

Solution steps

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

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

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

\int x y d z = x yz

= sin (x z) + x yz

Add a constant to the solution

= sin (x z) + x yz + C

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

\int \frac{x ^{2} + 3 x + 8}{x ^{3} - x ^{2} + 3 x - 3} d x

\int \frac{z ^{4} - 3 z ^{2} - 4 z}{5 z} d z

\int \frac{x}{( x + 1 ) - x + 1} d x

\int x + \frac{3 y}{x} d x

What is the integral of xcos(xz)+xy ?
The integral of xcos(xz)+xy is sin(xz)+xyz+C