New posts in Residue Calculus

Is there a direct proof for $\int_0^{2\pi}\frac{r^2+r(\cos t-\sin t)}{1+2r\cos t+r^2}dt=2\pi$

calculate: $\int_{-\infty}^{\infty}\frac{\cos\frac{\pi}{2}x}{1-x^{2}}dx$ using complex analysis ; detect my mistake

How to integrate $\int_0^\infty \left( \frac{\sin az}{z^2+1}\right)^2 dz$

Evaluate a real integral, e.g. $\int_{0}^{\infty}\frac{x^2}{(x^2+1)(x^2+4)}\:\mathrm dx$ with complex analysis

Is $\frac{\cos(\frac{1}{z})}{z^2}$ meromorphic or Not?

Residue Theorem if Pole is on Contour

Looking for a proof for the value of the residue.

Compute $\int_{\mathbb R}\frac{dx}{1+2x^2+x^4}$

Calculate the sum $\sum_{n=1}^\infty {(-1)^n\over 1+n^2}$

$2\pi i\beta = \int\limits_{|z|=r} \frac{dz}{f(z)-z}$