What is the integral of y*cos(y) ?

The integral of y*cos(y) is ysin(y)+cos(y)+C

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integral of y*cos(y)

\int y \cdot cos (y) d y

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

Solution steps

\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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