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I need a closed form using Mathematica or otherwise of the integral $$\int_{0}^{1} \frac{x\log x\log(\frac{1+x}{1-x})}{1-x^2} dx $$

This integral converges see here.

I am requesting a code with answer if possible in Wolfram Mathematica.

I am a beginner in Wolfram Mathematica.

Any help would be appreciated.

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  • $\begingroup$ Integrate[(x Log[x] Log[(1 + x)/(1 - x)])/(1 - x^2), {x, 0, 1}] gives 1/8 (-π^2 Log[4] + 7 Zeta[3]). $\endgroup$
    – Syed
    Mar 27, 2023 at 13:09
  • $\begingroup$ @Syed Thanks a lot $\endgroup$
    – Max
    Mar 27, 2023 at 13:10
  • $\begingroup$ If you have started learning Mathematica, then you will find that the introductory book written by the inventor is a good learning resource. There is a fast intro for math students as well as a fast intro for programmers to choose from. $\endgroup$
    – Syed
    Mar 27, 2023 at 13:11
  • $\begingroup$ Max, it is not the first post of this kind from you here. You have to do the typing. It looks like you are asking people to type your homeworks. $\endgroup$
    – yarchik
    Mar 27, 2023 at 13:22
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    $\begingroup$ You have a point @yarchik. $\endgroup$
    – Syed
    Mar 27, 2023 at 13:42

1 Answer 1

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Vs 13.2 gives

 Integrate[(x Log[x] Log[(1 + x)/(1 - x)])/(1 - x^2), {x, 0, 1}]



 1/8 (-\[Pi]^2 Log[4] + 7 Zeta[3])

You may enter the traditional form using e.g. the Menu/Palettes/BasicMathAssistant or with some typing experience you type 2d symbols by escape sequences

Esc dintt Esc

You will find out about all the shortcuts if you hover with the mouse over the BasicMathAssistant

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