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
Substitute:


 * $u = \tan x + \sec x$

Then from: we obtain:
 * Derivative of Tangent Function
 * Derivative of Secant Function
 * Linear Combination of Derivatives

Then: