x^n/(x+1)=x^(n-1)-x^(n-2)+---+(-1)^(n-1)+(-1)^n/(x+1)
∴I=∫x^n/(x+1) dx
=[x^n/n-x^(n-1)/(n-1)+---+(-1)^(n-1)x+(-1)^nIn|x+1|](0,1)（上下限）
=1/n-1/(n-1)+---+(-1)^(n-1)+(-1)^nIn2
=(-1)^(n-1)[1-1/2+1/3+---+(-1)^(n-1)/n]+(-1)^nIn2
又In(x+1)=x-x^2/2+x^3/3+---+(-1)^(n-1)x^n/n+---
令x=1 则In2=1-1/2+1/3+---+(-1)^(n-1)/n+---
∴limI=-(-1)^nIn2+(-1)^nIn2=0