Is this :$\int_{-1}^{1}\exp (-\tanh^{-1} (x))dx=\pi$ a well known integral representation for $\pi $?

Question

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 ?

score 0 · Answer 1 · 2018-07-21T02:36:03.343

0

Hint: $${{\tanh }^{-1}}\left( x \right)=\frac{1}{2}\ln \frac{1+x}{1-x}$$ check this link

edited Jul 21 '18 at 02:36

answered Jul 21 '18 at 02:29

you are right, probably it is a simplification for well known integral representations of pi – zeraoulia rafik Jul 21 '18 at 02:32
indded see the link in the answer – Jul 21 '18 at 02:37
Ok, I don't know if that was montioned in 16 formula representation of pi i linked above in question – zeraoulia rafik Jul 21 '18 at 02:44

Is this :$\int_{-1}^{1}\exp (-\tanh^{-1} (x))dx=\pi$ a well known integral representation for $\pi $?

1 Answers1