find the integral of sec^3x dx using the method of substitution

this isnt it try splitting it in two parts as sec^2x and secx now sec^2xdx can be written as d(tanx) and secx can be (1+tan^2x)^1/2 now multiply by 2 and divide by 2 then 2tanxd(tanx) can be written as d(1+tan^2x) now it might be simple foru let 1+tan^2x =y             can be solved now

put 3x=t

3dx=dt

=1/3 ln(sect+tant)

if it is sec³ x,then is the answer  ln(tan x)