∫(1/sinx)dx =∫1/[2sin(1/2)xcos(1/2)x]dx
=∫d(x/2)/[tan(x/2)(cos^2(x/2)]
=∫dtan(x/2)/tan(x/2)=Ln/tan(x/2)/+C
=Ln/cscx-cotx/+C