# Integration of 1 Over Square Root of (x^2-a^2)

In this tutorial we shall discuss the integration of 1 over square root of x^2-a^2, and this is another important for of integration.

The integration of $\frac{1}{{\sqrt {{x^2} - {a^2}} }}$ is of the form

To prove this formula, putting $x = a\cosh t$, we have $dx = a\sinh tdt$, $t = {\cosh ^{ - 1}}\left( {\frac{x}{a}} \right)$, so the given integral takes of the form

Using the value $t = {\cosh ^{ - 1}}\left( {\frac{x}{a}} \right)$, we have