Primitive of Secant Function/Secant plus Tangent Form

Theorem

 * $\displaystyle \int \sec x \ \mathrm d x = \ln \left \vert {\sec x + \tan x} \right \vert + C$

where $\sec x + \tan x \ne 0$.

Proof
Let:

Then:

Also see

 * Primitive of Cosecant Function