因为(1-cosx)=2sin(x/2)^2,所以原式＝x/2dcot(x/2)的积分,然后用分部积分法,原式＝(x/2)cot(x/2)-cot(x/2)d(x/2)的积分,后者的积分为ln|sin(x/2)|,结果为(x/2)cot(x/2)-ln|sin(x/2)|+c