令x=sinu,则√(1-x )=cosu,dx=cosudu ∫ √(1-x )dx =∫ (cosu) du(二倍角公式) =(1/2)∫ (1+cos2u)du =u/2+sin2u/4+C =(1/2) arcsinx+(1/2)x√(1-x )+C