(20) I = ∫ arctan√x * 2√xd√x/[√x(1+x)] = 2 ∫ arctan√x d√x/(1+x) 记 u = √x， 得 I = 2 ∫ arctanu du/(1+u^2) = 2 ∫ arctanu darctanu = (arctanu)^2 + C = (arctan√x)^2 + C
