When you see an integral with $\sin^m x$ and $\cos^p x$ in the numerator and denominator, check the difference in their powers. If the power of cosine in the denominator is 2 greater than the power of sine in the numerator, separating out a $\frac{1}{\cos^2 x}$ will always cleanly produce a $\tan$ and $\sec^2$ pair for an easy u-substitution.