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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: $$\int_0^\pi \frac{\sin^4(x)}{a+b\cos(x)}dx$$

$$\int_0^\frac{\pi}{2}\cos^{2n}(x)dx$$

Mahdi Ahmadi
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  • Have you calculated any integrals using complex analysis before? I would be more motivated to show you how to do if you showed some effort. Also, is this home work? – mickep Jan 15 '16 at 11:56
  • Hint: express the trigonometric functions in terms of $z=e^{i\theta}$. –  Jan 15 '16 at 11:56
  • yes it is a homework that my university professor gives me and i am search for its solution a lot and cant find it so i com to this site – Mahdi Ahmadi Jan 15 '16 at 12:18
  • The polynomial of degree seven you get in the first integral is actually of the form $z^5\cdot (\alpha z^2 + \beta z + \gamma)$, so to find the poles, you only need to find the zeros of the quadratic. Computing the residue at $0$ will be a little tedious. – Daniel Fischer Jan 15 '16 at 19:47

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