Complex analysis: Calculating $\int_{-\infty}^{\infty} \frac{\sin x}{x} dx$ by using $f(z) = \frac{e^{iz} - 1}{iz}$
60572
Computing $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x$ with residue calculus
23087
Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis
16820
Evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle
122843
Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
29425
$\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral
24182
Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
123694
How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
148746
Calculating $\int\frac{e^{iz}}{z}\, dz$ on the semi-circle given by $re^{i\theta}$ where $\theta:\,0\to\pi$
81258
Evaluation of $\int_{-\infty}^\infty \frac{\sin(at)}t\ dt$
100569
Evaluating the improper integral $\int_{0}^{\infty} \frac{x^3}{e^{x}-1} dx$
78712
Prove that $\frac{1}{\sin^2 z } = \sum\limits_{n= -\infty} ^ {+\infty} \frac{1}{(z-\pi n)^2} $
21240
Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
44737
$ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
68319
How can I evaluate $\int_{-\infty}^{\infty} e^{-x^2} dx$ without using polar coordinates
84826
Evaluating $\int_0^{2 \pi} e^{\cos x} \cos (nx - \sin x) \,dx$ using complex analysis