Newbetuts

The line integration of $\int_0^{2\pi} \frac{d \theta}{(z+a)(\bar z+\bar a)}$, where $|z|=1$ and $a \in \mathbb{C}$ with $|a|<1$ [duplicate]

Fundamental theorem of calculus for complex analysis, proof

Evaluating the integral $ \int_{-\infty}^{\infty} \frac{\cos \left(x-\frac{1}{x} \right)}{1+x^{2}} \ dx$

Prove that $\int_0^\infty\,\frac{\sin(kx)}{x(x^2+1)}\,\text{d}x=\frac{\pi}{2}\,\left(1-\exp(-k)\right)$ for all $k\in\mathbb{R}_{\ge0}$.

Scary contour integral, but is also an integral representation for $\Gamma$-function

Inequality for Distribution of points in space

Integral $\frac{1}{\pi}\int_0^{\pi/3}\log\big( \mu(\theta)+\sqrt{\mu^2(\theta)-1} \big)\ d\theta, \quad \mu(\theta)=\frac{1+2\cos\theta}{2}.$

Integral $ \int_0^\infty \frac{\ln(1+\sigma x)\ln(1+\omega x^2)}{x^3}dx$

How can i obtain general form of this integtral $\int_0^{\pi/4}\frac{x^3}{1+b\tan x}\ dx$

An integral $\int^\infty_0\frac{\tanh{x}}{x(1-2\cosh{2x})^2}{\rm d}x$

Complex analysis: Calculating $\int_{-\infty}^{\infty} \frac{\sin x}{x} dx$ by using $f(z) = \frac{e^{iz} - 1}{iz}$ [duplicate]

Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$

Integrating $\int_0^\infty \frac{\log x}{(1+x)^3}\,\operatorname d\!x$ using residues

Integral $I=\int_0^\infty \frac{\ln(1+x)\ln(1+x^{-2})}{x} dx$

New posts in contour-integration

Prove that $\int_0^\infty \frac{\ln x}{x^n-1}\,dx = \Bigl(\frac{\pi}{n\sin(\frac{\pi}{n})}\Bigr)^2$

Ramanujan's 'well known' integral, $\int\limits_{-\pi/2}^{\pi/2} (\cos x)^m e^{in x}dx$.

What contour should be used to evaluate $\int_0^\infty \frac{\sqrt{t}}{1+t^2} dt$

Show this $\int_0^\infty \frac{t\ln(2\sinh t)}{\left(3t^2+\ln^2(2\sinh t)\right)^2}~dt=0$

Contour integral representation of Confluent Hypergeometric Function

Calculating Inverse Laplace Transform of stretched exponential

The line integration of $\int_0^{2\pi} \frac{d \theta}{(z+a)(\bar z+\bar a)}$, where $|z|=1$ and $a \in \mathbb{C}$ with $|a|<1$ [duplicate]

Fundamental theorem of calculus for complex analysis, proof

Evaluating the integral $ \int_{-\infty}^{\infty} \frac{\cos \left(x-\frac{1}{x} \right)}{1+x^{2}} \ dx$

Prove that $\int_0^\infty\,\frac{\sin(kx)}{x(x^2+1)}\,\text{d}x=\frac{\pi}{2}\,\left(1-\exp(-k)\right)$ for all $k\in\mathbb{R}_{\ge0}$.

Scary contour integral, but is also an integral representation for $\Gamma$-function

Inequality for Distribution of points in space

Integral $\frac{1}{\pi}\int_0^{\pi/3}\log\big( \mu(\theta)+\sqrt{\mu^2(\theta)-1} \big)\ d\theta, \quad \mu(\theta)=\frac{1+2\cos\theta}{2}.$

Integral $ \int_0^\infty \frac{\ln(1+\sigma x)\ln(1+\omega x^2)}{x^3}dx$

How can i obtain general form of this integtral $\int_0^{\pi/4}\frac{x^3}{1+b\tan x}\ dx$

An integral $\int^\infty_0\frac{\tanh{x}}{x(1-2\cosh{2x})^2}{\rm d}x$

Complex analysis: Calculating $\int_{-\infty}^{\infty} \frac{\sin x}{x} dx$ by using $f(z) = \frac{e^{iz} - 1}{iz}$ [duplicate]

Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$

Integrating $\int_0^\infty \frac{\log x}{(1+x)^3}\,\operatorname d\!x$ using residues

Integral $I=\int_0^\infty \frac{\ln(1+x)\ln(1+x^{-2})}{x} dx$