What is the integral of ucos(u) ?

The integral of ucos(u) is usin(u)+cos(u)+C

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integral of ucos(u)

\int u cos (u) d u

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

Solution steps

\int u cos (u) d u

Apply Integration By Parts

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

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

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

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

Simplify

= u sin (u) + cos (u)

Add a constant to the solution

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

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