another problem
Didn't you post this earlier? Hmmm...Might have been someone else.
Anyway...
$\displaystyle \int \frac{dx}{x \sqrt{x^2 - 1}}$
Let $\displaystyle x = \frac{1}{t}$. Then $\displaystyle dx = -\frac{dt}{t^2}$.
$\displaystyle \int \frac{dx}{x \sqrt{x^2 - 1}} = \int \frac{ -\frac{dt}{t^2}}{ \frac{1}{t} \sqrt{ \frac{1}{t^2} - 1 } }$ $\displaystyle = - \int \frac{dt}{t \sqrt{\frac{1}{t^2} - 1}} = - \int \frac{dt}{\sqrt{t^2 \left ( \frac{1}{t^2} - 1 \right ) }}$
= $\displaystyle \int \frac{dt}{\sqrt{1 - t^2}}$
Do you recognize this integral?
-Dan