One of the methods that's normally used is the method of partial fractions to convert complex fractions into easier ones.

Yet in the following I've never seen this method applied to trig functions where it's also effective. So for example can you solve by partial fractions the following?:

If you can do the integration (which is solvable by other means, but the focus is on the method of partial fractions), then can you integrate the following also using the method of partial fractions?:

Please show all work, not just the answer.