tan^2x=sec^2x -1
∫tan^3x dx
=∫tanx(sec^2x -1) dx
=∫tanx sec^2x dx -∫tanxdx
=∫sinx/cos^3x dx -∫sinx/cosxdx
= 1/(2cos^2x)+ln |cosx|+c,c为常数∫sinx/cos^3x dx = 1/(2cos^2x)这部不明白你令t=cosx就明白了∫sinx/cos^3x dx= -∫1/cos^3x dcosx=-∫1/t^3 dt=1/(2t^2)在带回t=cosx就是了