$\displaystyle \int sin3x \\\ cosx \\\ dx $

I have been stuck on this question for some time, I initially used integration by parts, but this became very messy and confusing, I had to keep using integration by parts more than twice.

What is the correct method to use? Also I cant really think of any trig manipulation that I can do, to re-write sin3x.

Any help appreciated.

Thank you.