0≤x≤1∴1≤x+1≤2∴1/2·x^n≤x^n/(x+1)≤x^n∴∫[0~1]1/2·x^n·dx≤∫[0~1]x^n/(x+1)·dx≤∫[0~1]x^n·dx即：1/[2(n+1)]≤∫[0~1]x^n/(x+1)·dx≤1/(n+1)∵lim(n→∞)1/[2(n+1)]=0lim(n→∞)1/(n+1)=0根据夹逼准则，lim(n→∞)∫[0~1]x^n/(x+1)·dx=0
