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Math Help - An ambiguous integral involving logarithm

  1. #1
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    An ambiguous integral involving logarithm

    I get two different solutions for the integral

    \int_0^1 \frac{dx}{x} \ln \left( \frac{1+x}{1-x} \right) depending on how I evaluate it. Series expansion gives  \frac{\pi^2}{4} while Mathematica gives 1+2 \ln 2 as an analytical as well as a numerical solution. On the other hand, Wolfram Alpha also gives  \frac{\pi^2}{4}. I'm thinking that there must be some problem with singularities and/or (non)uniform convergence of the Taylor series for the logarithm.

    Any thoughts will be much appreciated.
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  2. #2
    A Plied Mathematician
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    Careful where your dx is, there. Can you give the command in Mathematica that gave you 1 + 2 ln(2)? I'm getting the first answer in Mathematica.
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  3. #3
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    Oops, I mistyped the integral in Mathematica. Silly me. It is indeed \frac{\pi^2}{4}.

    Thank you!
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  4. #4
    A Plied Mathematician
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    I figured.

    You're very welcome. Have a good one!
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