Convergence of $\int^\infty_0\frac{1}{1+x^2\sin^2(5x)}\,dx$
4220
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
65362
Does $\sum{\frac{\sin{(nx)}}{n}}$ converge uniformly for all $x$ in $[0,2\pi]$
91290
Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$
76756
A convergence proof: $\lim_{n\to\infty} \left(1+n^2\right)^{\frac1n}$
109718
Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)?
148443
convergence of infinite sum of integer values of integrable function
21375
The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
80428
Convergence of $\int\limits_1^{\infty}x^\alpha\sin(x^\beta)dx$
156231
Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
98247
Is $ \sum\limits_{n=1}^\infty \frac{|\sin n|^n}n$ convergent？
90558
A question related to a convergence of an integral
28666
simple convergence test $\lim_{n \to \infty} \frac{2^{n+1}+3^{n+1}}{2^n+3^n}$
56867
Convergence proof that involves integral
30439
Convergence of $\sum_{n=1}^{\infty}\frac{1}{n^\alpha}$
117264
Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$
76050
Test for convergence of the series $\sum_{n=1}^{\infty}\frac{n}{\sqrt{n^2 +1}}$
69808
For which values of $\alpha$ and $\beta$ does the integral $\int\limits_2^{\infty}\frac{dx}{x^{\alpha}\ln^{\beta}x}$ converge?