Use an indented contour and residues to establish the Cauchy principal value of $\int_{-\infty}^{\infty}\frac{\sin x}{x}$ using complex integration.
60572
Computing $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x$ with residue calculus
3068
Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?
109385
Evaluating the integral $\int_{-\ln 2}^{\ln 2} e^{-x}(\sin x+x)^{1/3}dx$
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
90095
Integrate $\int_0^{\infty } \frac{\cos x}{x} dx$
56836
Intuitive explanation of Cauchy's Integral Formula in Complex Analysis
10070
Complex analysis: Calculating $\int_{-\infty}^{\infty} \frac{\sin x}{x} dx$ by using $f(z) = \frac{e^{iz} - 1}{iz}$
100559
Gaussian integral with a shift in the complex plane
103487
Integration of the cardinal sine
61515
Evaluate $\int_0^{\infty} \frac{\log(x)dx}{x^2+a^2}$ using contour integration
70845
Contour method to show that $\int_0^\infty\frac{x-\sin x}{x^3} \, dx=\frac\pi4$
81258
Evaluation of $\int_{-\infty}^\infty \frac{\sin(at)}t\ dt$
17986
Contour method to solve $\int^\infty_0\frac{\ln(1+x)}{1+x^2}\,dx$
51284
$\int_{-\infty}^\infty \frac{e^{ax}}{1+e^x}dx$ with residue calculus
84267
Real integral by keyhole contour
142619
Evaluating the complex integral $\int_{|z|=2}^{}\frac{1}{z^2+1}dz$
89602
$ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $