What is the integral of usin(u) ?

The integral of usin(u) is -ucos(u)+sin(u)+C

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integral of usin(u)

\int u sin (u) d u

- u cos (u) + sin (u) + C

Solution steps

\int u sin (u) d u

Apply Integration By Parts

: - u cos (u) - \int - cos (u) d u

= - u cos (u) - \int - cos (u) d u

\int - cos (u) d u = - sin (u)

= - u cos (u) - (- sin (u))

Simplify

= - u cos (u) + sin (u)

Add a constant to the solution

= - u cos (u) + sin (u) + C

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