求s(积分号)1/【x^2*根号(2x^2-2x+1)】dx,

∫e^(2x)(tanx+1)^2dx
=∫e^2x(tanx^2+1)dx+∫e^2x*2tanxdx
=∫e^2xdtanx+∫tanxde^2x
=e^(2x)tanx-∫tanxde^2x+∫tande^2x+C
=e^(2x)tanx+C

∫e^x(1+sinx)dx/(1+cosx)
=∫e^xdx/(1+cosx)+∫e^xsinxdx/(1+cosx)
1+cosx=2cos(x/2)^2 sinx/(1+cosx)=tan(x/2)
=∫e^xd(x/2)/cos(x/2)^2+∫e^xtan(x/2)dx
=∫e^xdtan(x/2)+∫tan(x/2)de^x
=e^xtan(x/2)+C