简单分析一下，答案如图所示
令tan(x/2) = t 则sinx = 2t/(1+t²) x = 2arctant,dx = 2dt/(1+t²) ∫dx/(1+sinx) =∫2dt/(1+t)² =-2/(1+t) + C =-2/[1+tan(x/2)] + C
