∫tan^5xdx 过程 答案 谢谢

∫tan^5x dx
= ∫(tan³x)(tan²x) dx
= ∫tan³x*(sec²x-1) dx
= ∫tan³x*sec²x dx - ∫tan³x dx
= ∫tan³x dtanx - ∫(sec²x-1)*tanx dx
= (1/4)tan⁴x - ∫sec²x*tanx dx + ∫tanx dx
= (1/4)tan⁴x - ∫tanx dtanx - ∫d(cosx)/cosx
= (1/4)tan⁴x - (1/2)tan²x - ln|cosx| + C