What's the integration of the following trigonometric function

F(x) = (sec x)^3 (tan x)

Let u = sec(x), then du = sec(x) * tan(x) * dx

sec(x)^3 * tan(x) * dx =>
sec(x)^2 * sec(x) * tan(x) * dx =>
u^2 * du

Integrate

(1/3) * u^3 + C =>
(1/3) * sec(x)^3 + C