Prove or disprove the convergence of improper integral
83966
Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?
50682
Prove: $\lim\limits_{n \to \infty} \int_{0}^{\sqrt n}(1-\frac{x^2}{n})^ndx=\int_{0}^{\infty} e^{-x^2}dx$
107351
Evaluate the improper integral $\int_{0}^{\infty}{f(x)-f(2x)\over x}dx$, where $\lim_{x \to \infty} f(x) = L$
63756
Convergence or divergence of the integral $\int\limits_{10}^\infty \frac{e^x}{x^{1 + \frac{1}{x}} (e^x -1)} \,dx$
117486
Limit of uniformly continuous functions with convergent improper integrals.
90558
A question related to a convergence of an integral
58361
Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?
87169
Convergence of $\int_{1}^{\infty}x\cdot \sin{(e^x})\,dx$
35325
Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.
124498
Show that $\int_{-\infty}^{\infty} \dfrac{x^2}{(x^2+1)^2(x^2+2x+2)} \ dx$ is convergent.
142854
Convergence of Integrals - A Problem
39797
Convergence of integrals in $L^p$
19556
Finding constant to make integrals converge
146024
Help with counter-example on uniformly convergence.
25503
Convergence of $\sum_{n=1}^\infty \frac{\sin^2(n)}{n}$
125813
Convergence of $ \sum_{n=1}^\infty\left(\exp(\frac{(-1)^n}{n})-1\right)$?
139851
Test for divergence of $\int_{0}^{\infty} \frac{\sin^2(x)}{x}dx$ without evaluating the integral