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# 1,602 Reputation

65 Oct 9
 +10 02:02 upvote Two curious “identities” on $x^x$,$e$,and $\pi$ +10 02:01 upvote Definite Integral $\int_{-\pi}^{\pi}\frac{e^{\sin(x)+\cos(x)}\cos(\sin(x))}{e^{\sin(x)}+e^x}dx$ +10 01:53 upvote Prove $\sum_{i=1}^{n}\frac{x_{i}^3}{x_{i+1}^2}\geq \sum_{i=1}^{n}\frac{x_{i}^2}{x_{i+1}}$ +10 01:52 upvote Sum inequality: $\sum_{k=1}^n \frac{\sin k}{k} \le \pi-1$ +10 01:45 upvote How prove this $\tan{\frac{2\pi}{13}}+4\sin{\frac{6\pi}{13}}=\sqrt{13+2\sqrt{13}}$ +10 01:35 upvote Prove $\int_{0}^\infty \frac{1}{\Gamma(x)}\, \mathrm{d}x = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, \mathrm{d}x$ +5 02:02 upvote Two curious “identities” on $x^x$,$e$,and $\pi$
5 Oct 4
 +5 00:43 upvote Sphere Covering Problem
15 Oct 3
 +10 01:05 upvote How to prove $\frac{a}{a+bc}+\frac{b}{b+ac}+\frac{c}{c+ab}\geq \frac{3}{2}$ +5 17:27 upvote Square-free value of $n^2+1$ without large prime factors
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