令(x)^(1/2)=t∫x^(3/2)/(1+x) dx=∫2t^4dt/(1+t^2)=∫[2(t^2+1)^2-4(t^2+1)+2]dt/(1+t^2)=∫2(t^2+1)-4+2/(1+t^2)dt=2t^3/3-2t+2arctant+C故定积分的值为 pi/2-4/3
