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 Nov 27 comment Closed form of $\int_0^1\int_0^1\int_0^1\frac{\left(1-x^y\right)\left(1-x^z\right)\ln x}{(1-x)^3}\,\mathrm dx\;\mathrm dy\;\mathrm dz$ @0.5772156649... Yes, my new username means that I totally ceased sharing math knowledge in any math community since now on. Nov 10 awarded Good Question Nov 9 comment Calculating in closed form an integral in Airy function Good job there (+1) Oct 29 awarded Popular Question Oct 24 comment integral with square of log of a quadratic $\int_{0}^{1}\frac{\log^{2}(x^{2}-x+1)}{x}dx$ Good job!:D (+1) Oct 16 accepted The quadratic and cubic versions of a tough intregral Oct 6 comment How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$? Or more generally $$1\leq\ n^{\frac{1}{n}}\le (1+\epsilon)^{n^{\large \eta-1}}, \ \epsilon>0, 1>\eta>0$$ Oct 6 comment How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$? @Did Right. Alternatively, having in mind a similar idea, we see that $$1\leq\ n^{\frac{1}{n}}\le (1+\epsilon)^{\sqrt{n}/n}, \ \epsilon>0$$ for some $n\ge n_0$. Taking the limit as $n \to \infty$ we're done. Oct 5 comment Another beautiful integral (Part 2) A loooonnnnnnnnnnnggggggggggggg answer. Good job though!:-) (+1) Oct 1 comment Another beautiful integral (Part 2) @nospoon you made a lot of progress. Good job!(+1) Oct 1 comment Another beautiful integral (Part 2) @nospoon Try to add some spaces in the text and it will be fixed. Sep 30 comment Another beautiful integral (Part 2) @tired maybe there are very nice and short ways to do it. I feel I miss a nice way to go. Still working on it here. Sep 30 comment Another beautiful integral (Part 2) @nospoon very nice paper. Thanks (+1) Sep 30 comment Another beautiful integral (Part 2) @coffeemath also with Mathematica things become pretty complicated after $2$ integrations.The cases $n=2, 3$ are easy, but when dealing with $n\ge4$ the job to do is pretty difficult. Sep 30 revised Another beautiful integral (Part 2) added 190 characters in body Sep 30 asked Another beautiful integral (Part 2) Sep 27 accepted Another beautiful arctan integral $\int_{1/2}^1 \frac{\arctan\left(\frac{1-x^2}{7 x^2+10x+7}\right)}{1-x^2} \, dx$ Sep 27 comment Another beautiful arctan integral $\int_{1/2}^1 \frac{\arctan\left(\frac{1-x^2}{7 x^2+10x+7}\right)}{1-x^2} \, dx$ After cancelation, it remains $$\frac{1}{2}\left(\operatorname{Ti}_2\left(\frac{1}{6}\right)-\operatorname{Ti}‌​_2\left(\frac{1}{9}\right)\right)$$ I think. Sep 27 comment Another beautiful arctan integral $\int_{1/2}^1 \frac{\arctan\left(\frac{1-x^2}{7 x^2+10x+7}\right)}{1-x^2} \, dx$ (+1) for telling what Maple says. Sep 27 revised Another beautiful arctan integral $\int_{1/2}^1 \frac{\arctan\left(\frac{1-x^2}{7 x^2+10x+7}\right)}{1-x^2} \, dx$ added 1275 characters in body