Answer
$\ln 3$
Work Step by Step
Substitute into the relevant formula:
$\displaystyle \coth^{-1}(\frac{5}{4})=\frac{1}{2}\ln(\frac{\frac{5}{4}+1}{\frac{5}{4}-1})$
$=\displaystyle \frac{1}{2}\ln(\frac{\frac{9}{4}}{\frac{1}{4}})$
$=\displaystyle \frac{1}{2}\ln 9$
$=\displaystyle \frac{1}{2}\ln 3^{2}$
$=\ln 3$
