what is the integral of tan^3 x

the integration of tan^3 x is

-----> formula :::---

integral tan^n x = (1/n-1) tan^n-1 x - integral tan^n-2 x

here n=3

(1/3-1) tan^3-1 x -integral of tan^3-2 x

1/2 tan^2 x - integral tan x dx

1/2 tan^2 x - ln(cos x) +c

tan^3 x=tanx*tan^2 x = tanx(sec^2 x - 1) = tanx sec^2 x -tanx

Integration of this would give ( tanx) ^ 2/2 -log|sec x| +c