I have two integral that must solve with complex integrals
I know how to solve it in normal way but my university professor told me to solve it in complex integral solution way.
I know that it would solve by residue theorem but when I try to solve it in this way , a "seventh degree" term appears, which I can't handle.
I showed this problem to a math student and he can't solve it either.
I am an electrical engineering student and I am in my third year of university.
Please help me
the two integrals: $$\int_0^\pi \frac{\sin^4(x)}{a+b\cos(x)}dx$$
$$\int_0^\frac{\pi}{2}\cos^{2n}(x)dx$$