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

Explanation

`{:(int(x-1)/(sqrt(x^(2)-1))dx,"प्रथम समाकलन के लिये,"),(,"माना " x^(2)-1=t),(,2xdx=dt),(=int(x)/(sqrt(x^(2)-1))dx,rArr xdx=(dt)/(2)):}`
`-int(1)/(sqrt(x^(2)-1))dx`
`=(1)/(2)int(1)/(sqrtt)dt-int(1)/(sqrt(x^(2)-1^(2)))dx`
`=(1)/(2)int t^(-1//2)dt-int(1)/(sqrt(x^(2)-1^(2)))dx`
`=(1)/(2).(t^(1//2))/(1//2)-log|x+sqrt(x^(2)-1^(2))|+c`
`=sqrt(x^(2)-1)-log|x+sqrt(x^(2)-1)|+c`