I need to integrate , and I just cannot figure out what the trick is to it. I don't think it's any combination of integration by parts since will always stay the same and the other function will oscillate back and forth between sin and cosine, and all that will happen is that the factors of 5 will increase.

I also tried the double angle identity , and that resulted in the same kind of loop. I'm sure it's some little trick that I'm missing here, so any hints would be greatly appreciated.