Show without calculating that $\int_{-\infty}^{0} \frac{x^2}{(x^2+1)^2(x^2 + 2x + 2)} dx$ converges
124498
Show that $\int_{-\infty}^{\infty} \dfrac{x^2}{(x^2+1)^2(x^2+2x+2)} \ dx$ is convergent.
4220
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
61696
Prove that $\{x_1=1,\,x_{n+1}=\frac {x_n}2+\frac 1{x_n} \}$ converges when $n \to \infty$
18153
To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$
69978
Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
129823
Show that $\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})$ converges
76867
Does $\sum _{k=2} ^\infty \frac{(-1)^k}{\sqrt{k}+(-1)^k}$ converge conditionally?
124916
$f$ such that $\int_1^{\infty}f(x)dx$ converges, but not absolutely?
84765
Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
152648
Is the integral $\int_1^\infty\frac{x^{-a} - x^{-b}}{\log(x)}\,dx$ convergent?
87100
Decide whether $\sum_{n=1}^{\infty}(-1)^n\frac{nx}{1+n^4x^2}$ uniformly converges on $[0,\infty)$ or not
32042
Convergence of $\sum_{n=1}^\infty \frac{n^2}{2^n}$
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
56867
Convergence proof that involves integral
11435
Show that $\sum_{k=1}^\infty \frac{\ln{k}}{k^2}$ converges or diverges
149360
convergence of $ \sum_{k=1}^\infty \sin^2(\frac 1 k)$
17028
How to test if $\sum_{n=1}^{\infty }\frac{1}{n^{1+\frac{1}{n}}}$ converges?