令t=1+³√x，则x=(t-1)³，dx=3(t-1)²dtx=0时，t=1x=8时，t=3原式=∫(1~3)1/t·3(t-1)²dt=∫(1~3)(3t-6+3/t)dt=3/2·t²-6t+3lnt |(1~3)=(27/2-18+3ln3)-(3/2-6)=3ln3
