积分号1/sint dt怎么算

问题描述

精选答案

∫(1/sint)dt

=∫(sint/sin瞭)dt

=∫(sint)/(1-cos瞭)dt

=-∫[1/(1-cos瞭)]d(cost)

=(-1/2)∫[(1/1-cost)+(1/1+cost)]d(cost)

=(-1/2)[-ln|1-cost|+ln|1+cost|]+C

=(1/2)ln|(1-cost)/(1+cost)|+C