Hi, I just learned integration by parts. I'm trying to solve:

I know usually you want u to have the simpler derivative.

I set u=sin(3x+1), du=3cos(3x+1), v=(1/3)x^3, dv=x^2

So using integration by parts, uv- integral vdu

then I went through the steps to get my final answer:

Was my approach right? I wasn't too sure about this one...any help would be great.