∫(sinx/1+cosx)dx =-∫1/1+cosx d (cosx)=-∫1/1+cosx d (cosx+1)=-In|1+cosx|+c
∫(sinx)/(1+cosx)dx=∫(2sin(x/2)cos(x/2)/2cos(x/2)^2)dx=∫tan(x/2)dx=2∫tan(x/2)d(x/2)=-2∫cos(x/2)d(cos(x/2))=-2ln|cos(x/2)|+C