How to prove $\int_0^{\infty} \frac{\sin x}{x} \, dx = \frac{\pi}{2}$
3704
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
123899
$\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
139297
Find the sign of $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$
68821
Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$
76400
Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$
64480
How do I find $\int_{0}^{\infty} \frac{\sin^4 x}{x^2}\,dx$?
107296
How do I prove $\int_{-\infty}^{\infty}{\cos(x+a)\over (x+b)^2+1}dx={\pi\over e}{\cos(a-b)}$?
10547
$\int_0^\infty \frac{\sin(x^2+ax)}{x}\,dx$ converges
96191
Integral $\int_0^{\infty} \sin(x^2)/x^2\,dx$
10675
Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
101587
Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $
158279
$\int_0^{\pi/2}\ln(\sin(x))$?
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
130967
How to show that $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(4x)\cdots\sin(2^kx)\over x^{k+1}}\mathrm dx=2^{0.5(k^2-k-2)}\pi?$