答： 设x=sint,√(1-x²)=cost ∫ √(1-x²) dx =∫ cost d(sint) =∫ cos²t dt =∫ (cos2t+1)/2 dt =(1/4) ∫ cos2t+1 d(2t) =(1/4) (sin2t+2t)+C =(1/2)*[x√(1-x²)+arcsinx]+C
