secx^3(tan x) dx

I'm not sure if my work is correct, but I know the answer is right because I checked it in my book. Can someone check the work in blod type, please?

u = secx

du/dx = secxtanx

du = secxtanx dx

du/secx = tanx dx

u^3*du/secx

secx^3/secx du

secx^2 du

secx^3/3

1/3(secx^3) + C