What is the integral of-ysin(y) ?

The integral of-ysin(y) is ycos(y)-sin(y)+C

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integral of-ysin(y)

\int - y sin (y) d y

y cos (y) - sin (y) + C

Solution steps

\int - y sin (y) d y

Take the constant out:

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

= - \int y sin (y) d y

Apply Integration By Parts

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

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

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

Simplify

= y cos (y) - sin (y)

Add a constant to the solution

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