Primitive of Secant Function/Secant plus Tangent Form

Theorem

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

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

Proof
Substitute:


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

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

Then: