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

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

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integral of y*sin(y)

\int y \cdot sin (y) d y

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

Solution steps

\int y sin (y) d y

Apply Integration By Parts

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

= - 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

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What is the integral of y*sin(y) ?
The integral of y*sin(y) is -ycos(y)+sin(y)+C