For which $\alpha$, $\beta$ does $\int\limits_1^{\infty} x^{\alpha} \cdot (\ln x)^\beta dx$ converge?
69808
For which values of $\alpha$ and $\beta$ does the integral $\int\limits_2^{\infty}\frac{dx}{x^{\alpha}\ln^{\beta}x}$ converge?
69348
Prove that $\int \limits _{0}^{\infty}\frac{e^{-2x}-e^{-ax}}{x}\text{d}x$ converges for any $a>0$
63289
Does $\sum\limits_{x=1}^\infty\sin(x)$ converge?
44261
Convergence of $\sum^\infty_{n=1} \ln(1+\frac 1 {2^n})$
152105
When is $x^{\alpha}\sin(x^{\beta})$ uniformly continuous for $\alpha, \beta > 0$?
63756
Convergence or divergence of the integral $\int\limits_{10}^\infty \frac{e^x}{x^{1 + \frac{1}{x}} (e^x -1)} \,dx$
78008
A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
7042
Defined integral of $x^{\alpha} (1-x)^{\beta-1}$
114702
$\int_0^{\infty} f(x)dx$ converges and $\lim_{x\rightarrow \infty} f(x)$ exists, then $\lim_{x\rightarrow \infty} f(x)=0$?
54849
For what values of $\theta$ does $\sum_{1}^{\infty} \frac{e^{i n\theta}}{n}$ Converge?
41751
$\sum_{n=1}^\infty \frac{i^n}{n}$ converge?
97968
Does $\big|\sum_{k=1}^na_k\big|\leq\sqrt{n}$ imply the convergence of $\sum_{1}^\infty \frac{a_k}{k}$?
130241
What is the Convergence Radius and Domain of $\sum\limits_{n=0}^\infty \frac{1}{2^{n}} z^{2^n}$?
114673
Proving the convergence of $\sum_{n=2}^{\infty} \frac{1}{n (\ln n)^2}$
153267
Proving $\lim\limits_{x \to \infty} xf(x)=0$ if $\int_{0}^{\infty}f(x) dx$ converges.
22450
Convergence of $\sum\limits_{n=2}^\infty \frac{1}{n^\alpha \ln^\beta (n)} $ for nonnegative $\alpha$ and $\beta$
144795
Convergence or Divergence using Limits