Chapter 7.8, Problem 60PS

To determine

To prove:

  ${\displaystyle \int \frac{dx}{\sqrt{x^2+a^2}}}={\sinh }^{-1}\frac{x}{a}+c$ for constant $a>0$

  ${\displaystyle \int \frac{dx}{\sqrt{x^2-a^2}}}$ with $x>a>0$ .