用换元法
令√（1+e^x）=t,x=ln(t-1),dx=dt/(t-1)
x=ln3,t=2,x=ln8,t=3
∫[ln3,ln8]√（1+e^x）dx
=∫[2,3]t/(t-1)dt
=∫[2,3][1+1/(t-1)]dt
=[t+ln(t-1)][2,3]
=1+ln2