$\begin{align*} \int \frac{1}{x} \frac{\sqrt{x-1}}{x+1}dx \end{align*}$ is equal to :

Question

( A ) $\sinh^{-1}x - \sec^{-1} x +c$
( B ) $\sinh^{-1}x - \cos^{-1} x +c$
( C ) $\cosh^{-1}x + \sec^{-1} x +c$
( D ) $\cosh^{-1}x - \sec^{-1} x +c$