>173
tan(x/2) = t とおくと
1/sin(x) = (1+t^2)/2t,　dx = {2/(1+t^2)}dt,
　∫ {1/sin(x)}dx = ∫(1/t)dt = log|t| =log|tan(x/2)| = (1/2)log{[1-cos(x)]/[1+cos(x)]},