int sec^6(4x)tan(4x) dx Find the indefinite integral

Given to solve,
int sec^6 (4x)tan(4x) dx
let u = 4x , du = 4dx
so,
int sec^6 (4x)tan(4x) dx
= int sec^6 (u)tan(u) (du)/4
= (1/4) int sec^6 (u)tan(u) du
let secu = v
so, dv = (sec u)(tan u) du
so ,
(1/4) int sec^6 (u)tan(u) du
= (1/4) int sec^5 (u) tan(u) *sec(u) du
=(1/4) int (v)^5 dv
= (1/4) v^6/6
= (v^6)/24
= ((sec (u) )^6)/24
=((sec (4x) )^6)/24 +c