How to study the convergence of $\int^{\infty}_{0}\frac{2\cos(t)\sin(t)}{t}dt$?
22109
Convergence of $\int_0^\infty \sin(t)/t^\gamma \mathrm{d}t$
95353
Does $\sum_{n=1}^\infty \frac{\cos{(\sqrt{n})}}{n}$ converge?
141218
Does $\sum_{n=1}^{\infty} \frac{\sin(n)}{n}$ converge conditionally?
148443
convergence of infinite sum of integer values of integrable function
135840
Convergence\Divergence of $\sum\limits_{n=1}^{\infty}\frac {1\cdot 3\cdots (2n-1)} {2\cdot 4\cdots (2n)}$
10093
$\lim_{x\to \infty}e^{-x^2}\int_x^{x+1/x}e^{t^2}dt$
69348
Prove that $\int \limits _{0}^{\infty}\frac{e^{-2x}-e^{-ax}}{x}\text{d}x$ converges for any $a>0$
122950
Convergence of the $\sum_{n=1}^{\infty}n^3b_n^3$ where $b_n=\int_{-\pi}^{\pi}f(t)\sin (nt)\ dt$.
63612
Determine convergence of $\sum_{n=1}^{\infty}a_n$
121979
Pointwise convergence of sine series of $x^{-2}$
149850
Methods for determining the convergence of $\sum\frac{\cos n}{n}$ or $\sum\frac{\sin n}{n}$
157725
does $\int _{1}^{\infty}\frac{p(x)}{e^x}$ converge?
75459
study the convergence of $\sum_{n=1}^\infty \log \frac{n+1}{n}$
32423
Convergence of $\sum _{k=1}^\infty (1-\frac{1}{k})^{k^2}$
44261
Convergence of $\sum^\infty_{n=1} \ln(1+\frac 1 {2^n})$
42742
Is $\sum_{n=1}^\infty \frac{\sin(2n)}{1+\cos^4(n)}$ convergent?
16480
Does $\sum_{n=1}^{\infty}\ln(n\sin(\frac{1}{n}))$ converge?