Timeline for Integral $\int_0^1 \int_0^1 \cdots \int_0^1\frac{x_{1}^2+x_{2}^2+\cdots+x_{n}^2}{x_{1}+x_{2}+\cdots+x_{n}}dx_{1}\, dx_{2}\cdots \, dx_{n}=?$

3 events

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Dec 10, 2017 at 23:57	comment	added	Joe Silverman		In looking for patterns, it seems plausible that in the $n=4$ and $n=5$ formulas, the $\ln(2)$ term should be split into a multiple of $\ln(2)$ and a multiple of $\ln(4)$, and similarly in the $n=6$ formula some of the $\ln(2)$ and $\ln(3)$ terms should really be a $\ln(6)$ term. Possibly doing the computation by hand, rather than having Maple chunk out the answer, would give a plausible decomposition. Anyway, just a thought.
Dec 10, 2017 at 19:44	comment	added	Sylvain JULIEN		The last constant term seems to be $ -\frac{(n+1)(n-2)+1}{n+1} $ .
Dec 10, 2017 at 14:29	history	answered	Shahrooz	CC BY-SA 3.0