Indefinite integral problem

1. The problem statement, all variables and given/known data



Evaluate the indefinite integral of x*cos(3x)^2



2. Relevant equations



Integration by parts: [itex]\int(udv)[/itex]= uv - [itex]\int(vdu)[/itex]



3. The attempt at a solution



Im having trouble finding the antiderivative of cos(3x)^2 (which I designated as dv when doing integration by parts). I keep getting (1/9)(sin(3x)^3) using the power and chain rules, but that's not correct.



Thanks!