Primitive of Reciprocal of Cosine of a x

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Theorem

Logarithm of Secant plus Tangent Form

$\displaystyle \int \frac {\d x} {\cos a x} = \frac 1 a \ln \size {\sec a x + \tan a z}$


Logarithm of Tangent Form

$\displaystyle \int \frac {\mathrm d x} {\cos a x} = \frac 1 a \ln \left\vert{\tan \left({\frac \pi 4 + \frac {a x} 2}\right)}\right\vert + C$


Also see