Compute $\int_0^\infty \frac{\sin(x)}{x}dx$ without residue theorem.
3704
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
21240
Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only
29383
Computing $\int_{-\infty}^{\infty} \frac{\cos x}{x^{2} + a^{2}}dx$ using residue calculus
72039
Compute $\int_0^\infty\frac{\cos(xt)}{1+t^2}dt$
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
765
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
130967
How to show that $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(4x)\cdots\sin(2^kx)\over x^{k+1}}\mathrm dx=2^{0.5(k^2-k-2)}\pi?$
11129
Show that $\int_0^ \infty \frac{1}{1+x^n} dx= \frac{ \pi /n}{\sin(\pi /n)}$ , where $n$ is a positive integer.
123694
How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
109901
Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
3068
Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?
145183
finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis
50509
Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
77834
Is it possible to compute $\int_{-\infty}^\infty {x \sin x\over x^4+1}dx$ without using complex analysis?
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
39798
Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?
6573
Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$