分步积分u=x,v=ln(x+1),u导=1,v导=1/（x+1）.--------------- ,∫ln(x+1)dx=xln(x+1)-∫[x/(x+1)]dx=xln(x+1)-∫[1-1/(x+1)]dx=xln(x+1)-∫dx+∫1/(x+1)dx=xln(x+1)-x+ln(x+1)+C