Question

How do you find integral of x/root(x^2-1)dx ?

Answer 1

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

Explanation:

Subst.

`(x^2-1)=t^2. :. x^2=t^2+1. :. 2xdx=2tdt, or, xdx=tdt`

`:. I=intx/sqrt(x^2-1)dx`,

`=int(tdt)/sqrt(t^2)=int1dt=t`.

`rArr I=sqrt(x^2-1)+C.`