What is the integral of w^2sin(10w) ?

The integral of w^2sin(10w) is -1/10 w^2cos(10w)+1/500 (10wsin(10w)+cos(10w))+C

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integral of w^2sin(10w)

\int w^{2} sin (10 w) d w

- \frac{1}{10} w^{2} cos (10 w) + \frac{1}{500} (10 w sin (10 w) + cos (10 w)) + C

Solution steps

\int w^{2} sin (10 w) d w

Apply Integration By Parts

= - \frac{1}{10} w^{2} cos (10 w) - \int - \frac{1}{5} w cos (10 w) d w

\int - \frac{1}{5} w cos (10 w) d w = - \frac{1}{500} (10 w sin (10 w) + cos (10 w))

= - \frac{1}{10} w^{2} cos (10 w) - (- \frac{1}{500} (10 w sin (10 w) + cos (10 w)))

Simplify

= - \frac{1}{10} w^{2} cos (10 w) + \frac{1}{500} (10 w sin (10 w) + cos (10 w))

Add a constant to the solution

= - \frac{1}{10} w^{2} cos (10 w) + \frac{1}{500} (10 w sin (10 w) + cos (10 w)) + C

What is the integral of w^2sin(10w) ?
The integral of w^2sin(10w) is -1/10 w^2cos(10w)+1/500 (10wsin(10w)+cos(10w))+C