∫dx/sinx=∫sinxdx/(sinx)^2=-∫d(cosx)/[1-(cosx)^2]=-0.5∫[1/(1-cosx)+1/(1+cosx)] d(cosx)
=-0.5[ln|1+cosx|-ln|1-cosx|]+c
=-0.5ln|(1+cosx)/(1-cosx)|+c