Question

How do you find the integral of `dx /( (x^2)*sqrt((x^2)-1))`?

Answer 1

`sqrt(1-1/x^2) + C`

Explanation:

Finding this integral is easy by susbstituting `x= sectheta` so that `dx= sectheta tantheta d theta`

`int dx/(x^2* sqrt (x^2-1)`= #int (sectheta tan theta d theta)/(sec^2 theta tan theta#

=`int costheta d theta`= `sintheta +C`= `sqrt(1-1/x^2) + C`