You couldn't use the power rule on $\displaystyle x^{-u}$, because $\displaystyle u$ wasn't constant. However, because the function in question is a composition of functions, you use the chain rule. You can always use the chain rule on compositions of functions, unless there are domain/behavior issues (not likely encountered in Calc classes; such pathological behaviors are usually reserved for upper level courses in analysis). I like your $\displaystyle du/d\theta$ and your integrand. How do you propose to integrate?