1/2*x√(1-x^2)+1/2*arcsinx+C f(x)=∫ √(1-x^2) dx令x=sin t,则 sin2t=2x√(1-x^2) t=arcsin xf(x)=∫ cost d sint=∫ (cost)^2 dt=∫ (cos2t+1)/2 dt= 1/4*sin2t+t/2+C=1/2*x√(1-x^2)+1/2*arcsinx+C