∫sin^4x/cos^4xdx

Question

∫sin^4x/cos^4xdx
（网上没有请不要复制粘贴过来）

Answer 1

原式=∫tan^4xdx
=∫tan^2x*(sec^2x-1)dx
=∫tan^2x*sec^2xdx-∫tan^2xdx
=∫tan^2xd(tanx)-∫(sec^2x-1)dx
=(1/3)*tan^3x-tanx+x+C，其中C是任意常数

Answer 2

= ∫sin^4x/cos^4xdx
= ∫tan^4xdx
=(tan³x-3tanx十3x)/3十C追答

Answer 3

=∫sec²x(sec²x-1)-(sec²x-1)dx
=∫tan²xdtanx-tanx+x
=tan³x/3-tanx+x+C