Hyperbolic Inverse Functions

$\displaystyle \sinh^{-1} z$	$\textstyle =$	$\displaystyle \ln\left({z+\sqrt{z^2+1}\,}\right)$	(1)
$\displaystyle \cosh^{-1} z$	$\textstyle =$	$\displaystyle \ln\left({z\pm\sqrt{z^2-1}\,}\right)$	(2)
$\displaystyle \tanh^{-1} z$	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}\ln\left({1+z\over 1-z}\right)$	(3)
$\displaystyle \mathop{\rm csch}\nolimits ^{-1} z$	$\textstyle =$	$\displaystyle \ln\left({1\pm \sqrt{1+z^2}\,}\right)$	(4)
$\displaystyle \mathop{\rm sech}\nolimits ^{-1} z$	$\textstyle =$	$\displaystyle \ln\left({1\pm\sqrt{1-z^2}\over z}\right)$	(5)
$\displaystyle \coth^{-1} z$	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}\ln\left({z+1\over z-1}\right).$	(6)