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This question already has an answer here:

$$ \displaystyle \int_{0}^{1}\dfrac{\ln(x)\ln(1+x)\ln(1+x+x^{2})}{(1-x)(1+x^{2})}\,dx$$ I posted this on I&S but there was no response , so posting it here. Wolfram gave $-0.223434$, can it be evaluated in terms of special functions functions?

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marked as duplicate by Lucian, Nosrati, José Carlos Santos, hardmath, Namaste integration Sep 2 '17 at 0:05

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  • $\begingroup$ Why does this look like it can to you? It's not hard to write down an integral that can't be more simply represented $\endgroup$ – Brevan Ellefsen Apr 27 '17 at 16:48
  • $\begingroup$ Given that we are on $(0,1)$ where the natural logarithm has a simple, convergent Taylor Series we might be able to do this with a careful interchange of multi-summation and integration... Not sure what the best way to set this up would be though $\endgroup$ – Brevan Ellefsen Apr 27 '17 at 16:50
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    $\begingroup$ Question already asked: math.stackexchange.com/questions/2242141/… but not already solved $\endgroup$ – FDP Apr 28 '17 at 15:36
  • $\begingroup$ Note that there is now a bounty on that question @FDP hopefully someone can answer it. $\endgroup$ – Simply Beautiful Art Aug 19 '17 at 22:07