What is the integral of xycos(y) ?

The integral of xycos(y) is x(ysin(y)+cos(y))+C

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integral of xycos(y)

\int x y cos (y) d y

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

Solution steps

\int x y cos (y) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

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

= x (y sin (y) - (- cos (y)))

Simplify

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

Add a constant to the solution

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

What is the integral of xycos(y) ?
The integral of xycos(y) is x(ysin(y)+cos(y))+C