Show $\int _ 0 ^\infty \frac {\sin ( x^2 + ax )}{ x } dx$ converges for $a\ge 0$
10547
$\int_0^\infty \frac{\sin(x^2+ax)}{x}\,dx$ converges
152648
Is the integral $\int_1^\infty\frac{x^{-a} - x^{-b}}{\log(x)}\,dx$ convergent?
121979
Pointwise convergence of sine series of $x^{-2}$
133451
To show that ${x_n}$ is convergent where $|x_{n+1} - x_n|< \frac{1}{n^2}$
27192
$\sum|a_n|^2<\infty$ and $\sum a_n<\infty$ implies $\sum\log(1+a_n)$ converges
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
32042
Convergence of $\sum_{n=1}^\infty \frac{n^2}{2^n}$
129078
Proving the series $\sum_{n=0}^{\infty}\sin(e\pi n!)$ converges
91290
Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$
140220
Convergence of $\sum_{n=2}^{\infty}\frac{\sqrt{a_{n}}}{\ln\, n}(n^{a_{n}}-1)$
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
68097
Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
136421
How to prove convergence of $\sum\limits_{n=1}^\infty \frac{\sqrt a_n}{n^\alpha}$
27323
Convergence of the complex series $\sum_{n=0}^{\infty} \frac{(-1)^{n}}{z+n}$
90558
A question related to a convergence of an integral
158741
Convergence of $\sum \frac{a_n}{(a_1+\ldots+a_n)^2}$
16970
Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$