What is the integral of-ycos(y) ?

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

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integral of-ycos(y)

\int - y cos (y) d y

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

Solution steps

\int - y cos (y) d y

Take the constant out:

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

= - \int y cos (y) d y

Apply Integration By Parts

: y sin (y) - \int sin (y) d y

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

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

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

Simplify

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

Add a constant to the solution

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

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