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The integral $\displaystyle\int_0^1 \arcsin x \arctan x\log x dx$ can be explicitly computed; the result being representable in an elementary way (for instance without the appearance of polylogarithms). This was done around 2017. I would be interested in seeing a second generation proof. This problem was asked in a disguised form as problem 1431 in Elemente der Mathematik. No complete solution involving only elementary functions (roots and logarithms) was received.

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ray
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    It might be a good idea to give the closed form for the integral here (or did you intentionally exclude it for some reason?). It might also be a good idea to write out the integral in the title. – Christian E. Ramirez Oct 30 '23 at 18:20
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    @C-RAM I intentionally excluded the explicit form, as nested roots may have different representations – ray Oct 30 '23 at 18:29
  • @ray Can you give a link to it if not post it? – Тyma Gaidash Oct 30 '23 at 18:33
  • @ Tyma Gaidash Here are two sources: J.M. Campbell and A. Soho, in Integral Transforms and special functions 28 (2017). 547-559 and A. Stadler, Elemente der Mathematik 79 (2024), 38-44 (solution to problem 1431). – ray Feb 13 '24 at 16:01

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