I'm having trouble with the following integral:
$\int \frac{1}{\sqrt{a-x^{-1}}} \, dx.$
I attempted the substitution $u = a-x^{-1}$ to get
$\int \frac{1}{\sqrt{u} \, (a-u)^2} \, du,$
but I don't see where to go from there. Can someone give me a hint in the right direction?