What is the integral of rcos(r) ?

The integral of rcos(r) is rsin(r)+cos(r)+C

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integral of rcos(r)

\int r cos (r) d r

r sin (r) + cos (r) + C

Solution steps

\int r cos (r) d r

Apply Integration By Parts

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

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

= r sin (r) - (- cos (r))

Simplify

= r sin (r) + cos (r)

Add a constant to the solution

= r sin (r) + cos (r) + C