设e^x=t
则d(e^x)=dt
即e^xdx=dt
则dx=dt/e^x=dt/t
则
∫1/1+e^x dx
= ∫1/(1+t)*1/tdt
=∫[1/t-1/(1+t)]dt
=lnt-ln(1+t)+C
=lne^x-ln(1+e^x)+C
=x-ln(1+e^x)+C