∫e^2x/根号(e^x-1)dx
= ∫(e^x-1+1)/根号(e^x-1)d e^x
=∫根号(e^x-1)d e^x +∫1/根号(e^x-1)d e^x
=2/3*(e^x-1)^(3/2)+2*(e^x-1)^(1/2)+C