New posts in Contour Integration

Describing $\frac{\partial}{\partial x} \oint_{\partial \Omega(x)} f(x, n) \; \mathrm{d}n$ as a contour integral.

Residue Theorem Integral of $\frac{1}{\sinh(x)-1}$

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

Prove $ \int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$.

Evaluate $\int_0^1 \ln{\left(\Gamma(x)\right)}\cos^2{(\pi x)} \; {\mathrm{d}x}$

contour integration of $\int_0^\infty \frac{\ln(x)}{x^2-1}dx$

Methods to solve $\int _0^{\infty }\frac{x^{\frac{4}{5}}-x^{\frac{2}{3}}}{\ln \left(x\right)\left(x^2+1\right)}\:dx$

Proving $\int_0^{\pi} \frac{\log (1+r-2\sqrt{r}\cos(t))}{1+r-2\sqrt{r} \cos(t)}\,dt = \frac{2\pi}{1-r}\log(1-r)$, when $0 < r < 1$.

Residue Theorem if Pole is on Contour

Evaluation of $\int\limits ^{\infty }_{0}\frac{x}{\left( x^{2} +1\right)^2\left( e^{tx} +1\right)} dx$