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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
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