设u=tan(x/2),则cosx=(1-u^2)/(1+u^2),dx=2du/(1+u^2),
∫dx/(2+cosx)=∫2du/(3+u^2)
=(2/√3)∫d(u/√3)/(1+(u/√3)^2)
=(2/√3)arctan[tan(x/2)/√3]+C