令e^x=t，则x=lnt，dx=dt/t∫dx/(e^x+1) =∫dt/(1+t)t=∫(1/t-1/(1+t))dt=∫dt/t-∫dt/(1+t)=lnt-ln(1+t)+C=ln(t/(t+1))+C=ln(e^x/(e^x+1))+C
