I have tried to get interesting integral for interesting transcendental number , I have got the following :$\int_{-1}^{1}\exp (-\tanh^{-1} (x))dx=\pi$ , really I didn't accross that integral in the web as shown here, Now I ask if the titled integral is a well known integral representation or no , And how i can evaluate that ?
2026-03-25 11:06:41.1774436801
Is this :$\int_{-1}^{1}\exp (-\tanh^{-1} (x))dx=\pi$ a well known integral representation for $\pi $?
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Hint: $${{\tanh }^{-1}}\left( x \right)=\frac{1}{2}\ln \frac{1+x}{1-x}$$ check this link