Why does $\int_1^\infty \sin(x \log x)\,\mathrm{d}x$ converge?
134866
Does the integral $\int_{1}^{\infty} \sin(x\log x) \,\mathrm{d}x$ converge?
25503
Convergence of $\sum_{n=1}^\infty \frac{\sin^2(n)}{n}$
32436
Convergence of $\sum _{k=1}^\infty \sin \left(\sqrt{k}\right)/k$
43329
Why is $\int_{-1}^{1} \frac{1}x \mathrm{d}x$ divergent?
96505
Compute $\int_0^\infty \left(\frac{1}{x}\right)^{\ln(x)}\,\mathrm{d}x$
43576
Convergence of $\sum _{n=1}^{\infty }\left\{ 1-n\log \frac {2n+1} {2n-1}\right\} $
152648
Is the integral $\int_1^\infty\frac{x^{-a} - x^{-b}}{\log(x)}\,dx$ convergent?
109718
Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)?
10547
$\int_0^\infty \frac{\sin(x^2+ax)}{x}\,dx$ converges
110055
Convergence of the series $\sum_{n=1}^{\infty}((1/n)-\sin(1/n))$..?
100866
Why is $\int_{0}^{\infty} \frac {\ln x}{1+x^2} \mathrm{d}x =0$?
68866
Is $\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$ divergent or convergent?
103598
Showing that $\int_0^1 \log(\sin \pi x)dx=-\log2$
80465
Convergence/Divergence of $\sum_{n=1}^{\infty} \sin(1/n)$
147662
For what values $s$ does $\int_{0}^{\infty} \frac{\sin x}{x^s}dx$ converge?
29425
$\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral
5817
Does the series $\sum \limits_{n=2}^{\infty }\frac{n^{\log n}}{(\log n)^{n}}$ converge?