令√x=t,则x=t²,dx=2tdt原式=∫[0,1]2t³/(1+t)*dt=2∫[0,1][t²-t+1-1/(t+1)]dt=2/3*t³|[0,1]-t²|[0,1]+2t|[0,1]-2ln(1+t)|[0,1]=2/3-1+2-2ln2=ln4+5/3
