求不定积分∫ dx/(a+cosx)

设：t = tan(x/2) ,x = 2arctant ,dx = 2dt/(1+t^2) ,cosx = (1-t^2)/(1+t^2)I=∫ dx/(a+cosx)= ∫ 2dt/(a(1+t^2)+(1-t^2)=2∫dt/[(a-1)t^2+(a+1)]① a1 时：I = 2/(a+1) ∫dt/{[(a-1)/(a+1)]t^2+1}= 2/√(a^2-1) ∫...