New posts in contour-integration

How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?

Why is $\int_{[0,1]} \frac{dw}{1-wz}$ is holomorphic in unit disc?

How to compute $\int_0^{\infty} \frac{\sqrt{x}}{x^2-1}\mathrm dx$

An integral of rational function with third power of cosine hyperbolic function

Integral by residue - "dog bone"

How to prove error function $\mbox{erf}$ is entire (i.e., analytic everywhere)?

Integral with $\ln$ and rational function

integration using residue

contour integration of logarithm

Evaluating $\int_0^\infty \frac{\cos(ax)-e^{-ax}}{x \left(x^4+b^4 \right)}dx$

show that $\int_{0}^{\infty } \frac {\cos (ax) -\cos (bx)} {x^2}dx=\pi \frac {b-a} {2}$

Evaluate $\int_0^\infty \frac{(\ln x)^2}{x^2+4} \ dx$ using complex analysis.

$\int_{-\infty}^\infty \frac{\sin (t) \, dt}{t^4+1}$ must be zero and it isn't

Contour Integration $\int_0^1\frac1{\sqrt[n]{1-x^n}}dx$

Riemann's Trick with Hankel Contour

Integral with arctan and e: $\int_{0}^{\infty}\frac{\arctan(x^{3})}{e^{2\pi x}-1}\,\mathrm dx$

How to evaluate$J(k) = \int_{0}^{1} \frac{\ln^2x\ln\left ( \frac{1-x}{1+x} \right ) }{(x-1)^2-k^2(x+1)^2}\text{d}x$

Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$

Residue theorem:When a singularity on the circle (not inside the circle)

Residue theorem with $\frac{1}{2\pi}\int_{0}^{2\pi}e^{\cos\theta}\cos(n\theta) d\theta$.