`(1)/(sqrt((x-1)(x-b)))`

Explanation

`int(1)/(sqrt((x-1)(x-b)))dx`
`=int(1)/(sqrt(x^(2)-x(a+b)+ab))dx`
`=int(1)/(sqrt((x-(a+b)/(2))^(2)+ab-((a+b)^(2))/(4)))dx`
`=int(1)/(sqrt((x-(a+b)/(2))^(2)-((a-b)/(2))^(2)))dx`
`=log|x-(a+b)/(2)+sqrt((x-(a+b)/(2))^(2)-((a-b)/(2))^(2))|+c`
`=log|x-(a+b)/(2)+sqrt((x-a)(x-b))|+c`