求这题不定积分的详细解答过程

Question

如题所述

Answer 1

根据公式(secx)'=secxtanx
sec²=1十tan²x
∫tan^3(x)secxdx
=∫tan²xtanxsecxdx
=∫(sec²x-1)dsecx
=sec^3(x)/3-secx十C