`int1/(sqrt(x+a)+sqrt(x+b))\ dx`

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)/(a-b)[(x+a)^(3//2)-(x+b)^(3//2)]+C`