1. ## Complex plane integrals

1) $\oint_{\mid z+1\mid =1}\frac{dz}{z^{2}-1}$
2) $\oint_{\mid z-i\mid =2}\frac{sin(\pi z)}{z^{4}}dz$
3) $\int_{0}^{\pi}\frac{d \theta}{2+cos(\theta)}$
4) $\int_{- \infty}^{\infty}\frac{cos(x)}{x^{4}+1}dx$

Can you please tell me how can I find the value of these integrals? Just tell me how.

3. ## Re: Complex plane integrals

Are you sure? I think I should use Cauchy's residue theorem and Laurent series for 1), 2) and 4).

Cauchy's integral formula can be used for integrals like: $\oint_{\gamma} \frac{f(z)}{{(z-a)}^{n}}dz$