∫dx/sinx sinx=2sin(x/2)cos(x/2) 倍角公式
=∫ dx/(2*sin x/2*cos x/2) dx/2=d(x/2) sin(x/2)cos(x/2)=tan(x/2)(cosx/2)^2
=∫d(x/2) / (tan x/2*cos^2 x/2） d tan(x/2)=(sec(x/2))^2dx=dx/(cos(x/2))^2
=∫d(tan x/2) / tan x/2 dln(tan(x/2)=dtan(x/2)/tan(x/2)
=ln(tan(x/2))+C