How to show that $\int_{-\infty}^{\infty}|\frac{\sin{nx}\sin{x}}{x^2}|dx \to \infty$ as $n \to \infty$?
63453
A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$
23685
Integrating $\int \sin^n{x} \ dx$
65337
Compute $\int_{0}^{\infty}\frac{x\sin 2x}{9+x^{2}} \, dx$
20016
How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$?
77834
Is it possible to compute $\int_{-\infty}^\infty {x \sin x\over x^4+1}dx$ without using complex analysis?
158279
$\int_0^{\pi/2}\ln(\sin(x))$?
87242
Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
129734
Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
64480
How do I find $\int_{0}^{\infty} \frac{\sin^4 x}{x^2}\,dx$?
49074
Compute $\int\limits_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx$ via residue calculus.
11489
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
51284
$\int_{-\infty}^\infty \frac{e^{ax}}{1+e^x}dx$ with residue calculus
62173
How do I show that $\int_0^\infty \frac{\sin(ax) \sin(bx)}{x^{2}} \, \mathrm dx = \pi \min(a,b)/2$
148743
$\int_0^\infty \frac{1}{1+x^ 9} \, dx$
109606
Detail in the use of the Residue Theorem for $\int\limits_{-\infty}^{\infty}\frac{\cos(2x)-1}{x^2}dx$
147662
For what values $s$ does $\int_{0}^{\infty} \frac{\sin x}{x^s}dx$ converge?
39798
Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?