Prove that $ \int_0^\infty (\frac{\sin x}{x})^2 = \frac{\pi}{2}$.
10036
Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$
96388
Prove $\sin(x)\tan(x) > x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$
84765
Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
123899
$\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
96191
Integral $\int_0^{\infty} \sin(x^2)/x^2\,dx$
128572
How $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}$ exists?
68821
Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$
51837
Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
104904
Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem.
141516
Solve $\int_0^{+\infty} \Big(\frac{\sin t}{t}\Big)^2 \ dt$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
1057
How prove this integral limit $=f(\frac{1}{2})$
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
67622
Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$
58646
Are there any ways to evaluate $\int^\infty_0\frac{\sin x}{x}dx$ without using double integral?
139453
Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$