What is the integral of y^2sin(8y) ?

The integral of y^2sin(8y) is -1/8 y^2cos(8y)+1/256 (8ysin(8y)+cos(8y))+C

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integral of y^2sin(8y)

\int y^{2} sin (8 y) d y

- \frac{1}{8} y^{2} cos (8 y) + \frac{1}{256} (8 y sin (8 y) + cos (8 y)) + C

Solution steps

\int y^{2} sin (8 y) d y

Apply Integration By Parts

= - \frac{1}{8} y^{2} cos (8 y) - \int - \frac{1}{4} y cos (8 y) d y

\int - \frac{1}{4} y cos (8 y) d y = - \frac{1}{256} (8 y sin (8 y) + cos (8 y))

= - \frac{1}{8} y^{2} cos (8 y) - (- \frac{1}{256} (8 y sin (8 y) + cos (8 y)))

Simplify

= - \frac{1}{8} y^{2} cos (8 y) + \frac{1}{256} (8 y sin (8 y) + cos (8 y))

Add a constant to the solution

= - \frac{1}{8} y^{2} cos (8 y) + \frac{1}{256} (8 y sin (8 y) + cos (8 y)) + C

What is the integral of y^2sin(8y) ?
The integral of y^2sin(8y) is -1/8 y^2cos(8y)+1/256 (8ysin(8y)+cos(8y))+C