Integrate: $\int_0^\infty \frac{\sin^2(x)}{x^2}dx$
10036
Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$
130736
Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
117113
Integration of $x^2 \sin(x)$ by parts
4220
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
76129
Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
48233
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
117587
$\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$
69978
Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
63650
Evaluating the contour integral $\int_{0}^{\infty}\frac{\sin^{3}(x)}{x^{3}}\mathrm dx$
41447
tough integral involving $\sin(x^2)$ and $\sinh^2 (x)$
35861
Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
106812
Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
123899
$\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
83966
Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?
72036
Closed form of $\int_0^\infty \sin(x)\sin\left(\frac{1}{x}\right)dx$?
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
765
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues