Prove that $\int_0^{\infty}\sin(x^2)dx$ converges.
122233
Trig Fresnel Integral
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
87169
Convergence of $\int_{1}^{\infty}x\cdot \sin{(e^x})\,dx$
87242
Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
157422
Why $\sin(nx)$ converges weakly in $L^2(-\pi,\pi)$?
129078
Proving the series $\sum_{n=0}^{\infty}\sin(e\pi n!)$ converges
63237
Proving that $\lim_{n \rightarrow\infty} \int_{0}^{\frac{\pi}{2}} \sin(t^n) dt =0$
45205
Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
68866
Is $\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$ divergent or convergent?
157725
does $\int _{1}^{\infty}\frac{p(x)}{e^x}$ converge?
6990
For $f$ Riemann integrable prove $\lim_{n\to\infty} \int_0^1x^nf(x)dx=0.$
116498
Convergence of improper integral $\int_{0}^{1}\frac{\log(x)}{1-x^2}dx$
147662
For what values $s$ does $\int_{0}^{\infty} \frac{\sin x}{x^s}dx$ converge?
53105
How to prove that this sequence converges? $\sum_{n=1}^{\infty} \frac{1}{n\ln^2(n)}$
39798
Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
97039
Use integral test to show that Gaussian Integral $\int_{-\infty}^{\infty} e^{-x^2} \ dx$ converges?