I can not seem to figure out why Arctanh x [ Hyperbolic Arctan ]

can be expressed as

Arctanh x = (1/2) [ Log (1+x) - Log (1-x) ]

Note; I know the 1/2 means the expression is a square root

of the ratio of the 2 binomials and has been taken out with the Power Rule

Can anyone show me the connection ?

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Note the above has been corrected for errors from the original post

can be expressed as

Arctanh x = (1/2) [ Log (1+x) - Log (1-x) ]

Note; I know the 1/2 means the expression is a square root

of the ratio of the 2 binomials and has been taken out with the Power Rule

Can anyone show me the connection ?

===================================================

Note the above has been corrected for errors from the original post

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