Leave the first term as it is, since you're trying to find a solution in terms of , since
So the integral is now:
Carry out integration by parts on the 2nd term of the integral and again try to manipulate it so that you get an expression in terms of . You should then be able to factor out of the whole expression, and the multiple should be .
Hint: When it comes to integrating that term by parts, it is difficult to integrate , hence that is the term you should differentiate!