y=In(e^x-1)
令t= e^x-1dt=d(e^x-1) dt=e^xdx
y=lnt
dy=dlnt
dy=1/tdt
将t= e^x-1 dt=e^xdx 代入dy=1/tdt
dy=(1/(e^x-1))e^xdx
dy=e^x/(e^x-1)dx
dy/dx=e^x/(e^x-1)