Prove or disprove $\int^{\infty}_{0}(\prod^{n}_{r=1}\cos\frac{x}{r})\frac{\sin(4x)}{x}dx=\frac{\pi}{2}$
34650
Explain why $\int_0^\infty\frac{\sin{4x}}{x}\prod\limits_{k=1}^n \cos\left(\frac{x}{k}\right) dx\approx\frac{\pi}{2}$
24182
Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
96961
A proof for the identity $\sum_{n=r}^{\infty} {n \choose r}^{-1} = \frac{r}{r-1}$
3527
Finding $\lim_{n \to \infty} \prod_{r=1}^n (1+ \frac{1}{a_r})$
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
13796
What is the value of $\prod_{n=1}^\infty (1+\frac{1}{n^2})$?
70845
Contour method to show that $\int_0^\infty\frac{x-\sin x}{x^3} \, dx=\frac\pi4$
11129
Show that $\int_0^ \infty \frac{1}{1+x^n} dx= \frac{ \pi /n}{\sin(\pi /n)}$ , where $n$ is a positive integer.
52311
Prove that $0 \le \frac{1+\cos\theta}{2+\sin\theta} \le \frac{4}{3}$ for all real $\theta$.
151127
Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
129042
Prove that $\lim_{a \to 0^{+}} \int_{0}^{a} \frac{1}{\sqrt{\cos(x)-\cos(a)}} \;dx=\frac{\pi}{\sqrt{2}}$
4287
Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
70715
How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$?
68858
Prove that $\prod_{n=2}^∞ \left( 1 - \frac{1}{n^4} \right) = \frac{e^π - e^{-π}}{8π}$
5402
Prove or the disprove the existence of a limit of integrals
78712
Prove that $\frac{1}{\sin^2 z } = \sum\limits_{n= -\infty} ^ {+\infty} \frac{1}{(z-\pi n)^2} $
83280
Infinite product $ \prod^{\infty}_{n=0}\left(1-\frac{1}{2^{3n}}-\frac{1}{2^{6n}}\right)$