What is the integral of y^2cos(y) ?

The integral of y^2cos(y) is y^2sin(y)-2(-ycos(y)+sin(y))+C

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integral of y^2cos(y)

\int y^{2} cos (y) d y

y^{2} sin (y) - 2 (- y cos (y) + sin (y)) + C

Solution steps

\int y^{2} cos (y) d y

Apply Integration By Parts

= y^{2} sin (y) - \int 2 y sin (y) d y

\int 2 y sin (y) d y = 2 (- y cos (y) + sin (y))

= y^{2} sin (y) - 2 (- y cos (y) + sin (y))

Add a constant to the solution

= y^{2} sin (y) - 2 (- y cos (y) + sin (y)) + C

What is the integral of y^2cos(y) ?
The integral of y^2cos(y) is y^2sin(y)-2(-ycos(y)+sin(y))+C