Does $\int _1^{\infty }\left(\sin \left(x^2\right)\right)dx$ converge or diverge?
301
Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.
88792
Convergence of $\int_0^\infty $sin$ (x^p) dx$
109718
Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)?
35435
For what values of $\alpha$, does this integral converge?
58475
Does $\int_0^\infty |\cos(x^2)| \mathrm dx$ converge?
80465
Convergence/Divergence of $\sum_{n=1}^{\infty} \sin(1/n)$
10036
Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$
42742
Is $\sum_{n=1}^\infty \frac{\sin(2n)}{1+\cos^4(n)}$ convergent?
110055
Convergence of the series $\sum_{n=1}^{\infty}((1/n)-\sin(1/n))$..?
16480
Does $\sum_{n=1}^{\infty}\ln(n\sin(\frac{1}{n}))$ converge?
124916
$f$ such that $\int_1^{\infty}f(x)dx$ converges, but not absolutely?
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
117583
Why does $\sum_{n=0}^\infty (\sin{\frac{1}{n}})(\sinh{\frac{1}{n}})(\cos n)$ converge
62443
Prove that $\sum_{n=1}^\infty \ln\left(\frac{n(n+2)}{(n+1)^2}\right)$ converges and find its sum
121971
How to test the convergence for $\sum _{n=3}^{\infty }\:\left(-\frac{1}{\sqrt{ln\left(n\right)}}\right)^{n+1}$?
122073
Computing $\lim_{n \rightarrow\infty} \int_{a}^{b}\left ( f(x)\left | \sin(nx) \right | \right )$ with $f$ continuous on $[a,b]$
26370
Consider convergence of series: $\sum_{n=1}^{\infty}\sin\left[\pi\left(2+\sqrt{3}\right)^n\right]$