Does the improper integral $\int_0^\infty |\sin (x^2)| \; dx$ converge?
58475
Does $\int_0^\infty |\cos(x^2)| \mathrm dx$ converge?
91290
Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$
88597
Improper integral from 1 to infinity $\Rightarrow$ integrated function converges towards zero?
58361
Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?
8934
How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?
4220
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
80465
Convergence/Divergence of $\sum_{n=1}^{\infty} \sin(1/n)$
97039
Use integral test to show that Gaussian Integral $\int_{-\infty}^{\infty} e^{-x^2} \ dx$ converges?
16480
Does $\sum_{n=1}^{\infty}\ln(n\sin(\frac{1}{n}))$ converge?
110394
For which values this integral converge?
87169
Convergence of $\int_{1}^{\infty}x\cdot \sin{(e^x})\,dx$
6345
Is the $\sum\sin(n)/n$ convergent or divergent?
65362
Does $\sum{\frac{\sin{(nx)}}{n}}$ converge uniformly for all $x$ in $[0,2\pi]$
83191
improper integrals (comparison theorem)
119898
necessary condition of improper integral
104904
Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem.
63756
Convergence or divergence of the integral $\int\limits_{10}^\infty \frac{e^x}{x^{1 + \frac{1}{x}} (e^x -1)} \,dx$