Integrating $ \int \limits_{-\infty}^{\infty} \frac{\sin^2(x)}{x^2} \operatorname d\!x $
10036
Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$
128572
How $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}$ exists?
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
111636
Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$
104138
How to integrate $\int\limits_0^\infty e^{-a x^2}\cos(b x) dx$ where $a>0$
6014
Evaluating $\int_{-\infty}^{\infty}\frac{\exp\left(-a x^2\right)}{x^2+b^2}dx$
109606
Detail in the use of the Residue Theorem for $\int\limits_{-\infty}^{\infty}\frac{\cos(2x)-1}{x^2}dx$
99457
How to integrate $\int x\sin {(\sqrt{x})}\, dx$
63650
Evaluating the contour integral $\int_{0}^{\infty}\frac{\sin^{3}(x)}{x^{3}}\mathrm dx$
72036
Closed form of $\int_0^\infty \sin(x)\sin\left(\frac{1}{x}\right)dx$?
4220
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
90095
Integrate $\int_0^{\infty } \frac{\cos x}{x} dx$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
152339
Complex-valued Fourier integral: $ \int_{ - \infty }^{ + \infty } {\frac{{\cos (ax)}}{{{x^2} + 1}}{e^{ - ibx}}\,\mathrm dx} $
93071
Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$?
68866
Is $\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$ divergent or convergent?
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$