∫e^xdx/(1+cosx)+∫e^xsinxdx/(1+cosx)=∫e^xdtan(x/2)+∫tan(x/2)de^x=e^x tan(x/2) -∫tan(x/2)de^x+∫tan(x/2)de^x+C=e^x tan(x/2) +C
