How to calculate this integral with square roots: $\int\frac{ \sqrt{x+1} }{ \sqrt{ x-1 }} \, dx$ How would you calculate this integral:
$$\int_{}\frac{ \sqrt{x+1} }{ \sqrt{ x-1 }} \, dx$$

HINT:
$$\sqrt{\dfrac{x+1}{x-1}}=u\implies x=\dfrac{u^2+1}{u^2-1}=1+\dfrac2{u^2-1}$$
and use Partial Fraction Decomposition 
