令t=e^x,得
原式=∫1/[t(t+t^(-1))^2]dt
=∫t/(t^4+2t^2+1)dt
=(1/2)∫1/(t^2+1)^2d(t^2+1)
=-1/[2(t^2+1)]+C
=-1/[2(e^2x+1)]+C