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

The integral of y^2sin(2y) is -1/2 y^2cos(2y)+1/4 (2ysin(2y)+cos(2y))+C

integral of y^2sin(2y)

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

- \frac{1}{2} y^{2} cos (2 y) + \frac{1}{4} (2 y sin (2 y) + cos (2 y)) + C

Solution steps

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

Apply Integration By Parts

= - \frac{1}{2} y^{2} cos (2 y) - \int - y cos (2 y) d y

\int - y cos (2 y) d y = - \frac{1}{4} (2 y sin (2 y) + cos (2 y))

= - \frac{1}{2} y^{2} cos (2 y) - (- \frac{1}{4} (2 y sin (2 y) + cos (2 y)))

Simplify

= - \frac{1}{2} y^{2} cos (2 y) + \frac{1}{4} (2 y sin (2 y) + cos (2 y))

Add a constant to the solution

= - \frac{1}{2} y^{2} cos (2 y) + \frac{1}{4} (2 y sin (2 y) + cos (2 y)) + C

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What is the integral of y^2sin(2y) ?
The integral of y^2sin(2y) is -1/2 y^2cos(2y)+1/4 (2ysin(2y)+cos(2y))+C