What is the integral of u^2sin(5u) ?

The integral of u^2sin(5u) is -1/5 u^2cos(5u)+2/125 (5usin(5u)+cos(5u))+C

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integral of u^2sin(5u)

\int u^{2} sin (5 u) d u

- \frac{1}{5} u^{2} cos (5 u) + \frac{2}{125} (5 u sin (5 u) + cos (5 u)) + C

Solution steps

\int u^{2} sin (5 u) d u

Apply Integration By Parts

: - \frac{1}{5} u^{2} cos (5 u) - \int - \frac{2}{5} u cos (5 u) d u

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

\int - \frac{2}{5} u cos (5 u) d u = - \frac{2}{125} (5 u sin (5 u) + cos (5 u))

= - \frac{1}{5} u^{2} cos (5 u) - (- \frac{2}{125} (5 u sin (5 u) + cos (5 u)))

Simplify

= - \frac{1}{5} u^{2} cos (5 u) + \frac{2}{125} (5 u sin (5 u) + cos (5 u))

Add a constant to the solution

= - \frac{1}{5} u^{2} cos (5 u) + \frac{2}{125} (5 u sin (5 u) + cos (5 u)) + C

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What is the integral of u^2sin(5u) ?
The integral of u^2sin(5u) is -1/5 u^2cos(5u)+2/125 (5usin(5u)+cos(5u))+C