# Math Help - An ambiguous integral involving logarithm

1. ## 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.

2. 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.

3. Oops, I mistyped the integral in Mathematica. Silly me. It is indeed $\frac{\pi^2}{4}$.

Thank you!

4. I figured.

You're very welcome. Have a good one!