Show that $\int\nolimits^{\infty}_{0} x^{-1} \sin x dx = \frac\pi2$
3704
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
80553
Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
42805
Show that $\int\limits_0^1 \left(x^{x}\right)^{\left(x^{x}\right)^{\left(x^{x}\right)^{\left(x^{x}\right)^{⋰}}}}\ \mathrm{d}x=\frac{\pi^2}{12}$.
156231
Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
123899
$\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
78008
A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
68097
Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
4287
Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
152640
show that $\lim(\pi(x)/x) = 0$
142114
Limit as $x\to 2$ of $\frac{\cos(\frac \pi x)}{x-2} $
158279
$\int_0^{\pi/2}\ln(\sin(x))$?
130967
How to show that $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(4x)\cdots\sin(2^kx)\over x^{k+1}}\mathrm dx=2^{0.5(k^2-k-2)}\pi?$
103513
Show that $\lim_{n\to \infty}\int_{-\pi}^{\pi}f(x)g(nx)\,dx=\frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)\,dx\int_{-\pi}^{\pi}g(x)\,dx$
117246
Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$.
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
53307
how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
98836
Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$