计算定积分∫(0,e-1)ln(x+1)dx
问题描述：
计算定积分∫(0,e-1)ln(x+1)dx
答
∫(0,e-1)ln(x+1)dx
=xln(x+1)|(0,e-1) -∫(0,e-1)xdln(x+1)
=(e-1)-∫(0,e-1)x/(x+1) dx
=(e-1)-∫(0,e-1) dx +∫(0,e-1)(1/(x+1))dx
=2(e-1)-ln(x+1)|(0,e-1)
=2(e-1)+1
=2e-1