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: Multiply top and bottom by $\sqrt{x+1}$. So we want
$$\int \frac{x+1}{\sqrt{x^2-1}}\,dx.$$
Now let $x=\cosh t$.
