记I=∫sec^3(x) dx,则I=∫sec(x)*sec^2(x) dx=∫sec(x)*[tan(x)]' dx=sec(x)*tan(x)-∫[sec(x)]'*tan(x) dx（分部积分）=sec(x)*tan(x)-∫[sec(x)*tan(x)]*tan(x) dx=sec(x)*tan(x)-∫sec(x)*tan^2(x) dx=sec(x)*tan...