`(1)/(sqrt(x+a)+sqrt(x+b))`

Explanation

`int(1)/(sqrt(x+a)+sqrt(x+b))dx`
`=int(1)/(sqrt(x+a)+sqrt(x+b))xx(sqrt(x+a)-sqrt(x+b))/(sqrt(x+a)-sqrt(x+b))dx`
`=int(sqrt(x+a)-sqrt(x+b))/((x+a)-(x+b))dx`
`=(1)/(a-b)int{(x+a)^(1//2)-(x+b)^(1//2)}dx`
`=(1)/(a-b){((x+a)^((1//2)+1))/((1)/(2)+1)-((x+b)^((1//2)+1))/((1)/(2)+1)}+C`
`=(1)/(a-b){((x+a)^(3//2))/(3//2)-((x+b)^(3//2))/(3//2)}+C`
`=(2)/(3(a-b))[(x+a)^(3//2)-(x+b)^(3//2)]+C`