解法一：求出f(x),进而对f(x)进行积分。求出f(x),进而对f(x)进行积分。求出f(x),进而对f(x)进行积分。令ln⁡x=t,原式f(t)=ln⁡(1+et)et令\lnx=t,原式f(t)=\frac{\ln(1+e^t)}{e^t}令lnx=t,原式f(t)=etln(1+et)​则∫f(x) dx=∫ln⁡(1+ex)ex dx=∫ln⁡(1+ex)e−x dx则\intf(x)\,{\rmd}x=\int\frac{\ln(1+e^x)}{e^x}\,{\rmd}x\\=\int\ln(1+e^x)e^{-x}\,{\rmd}x则∫f(x)dx=∫exln(1+ex)​dx