分部积分法：∫x/(1-cosx)dx=∫0.5x/(sinx/2)^2dx=-∫xd(ctgx/2)=-xctg(x/2)+∫ctg(x/2)dx=-xctg(x/2)+∫cos(x/2)/sin(x/2)dx=-xctg(x/2)+2∫d(sin(x/2)/sin(x/2)=-xctg(x/2)+2ln|sinx/2|+C