int dx/((x + 1)^(1/2) - x^(1/2)) =
= int ((x+1)^(1/2) + x^(1/2)) dx/(((x + 1)^(1/2) - x^(1/2)) * ((x+1)^(1/2) + x^(1/2))) =
= int ((x + 1)^(1/2) + x^(1/2)) dx/(x + 1 - x) = int ((x + 1)^(1/2) + x^(1/2)) dx =
= int (x + 1)^(1/2) dx + int x^(1/2) dx =
= 1/(1/2 + 1) * (x + 1)^(1/2 + 1) + 1/(1/2 + 1) * x^(1/2 + 1) + C =
= 2/3 * (x + 1)^(3/2) + 2/3 * x^(3/2) + C