Primitive of Reciprocal of Cosine of a x

Theorem

Logarithm of Secant plus Tangent Form

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

Logarithm of Tangent Form

$\ds \int \frac {\d x} {\cos a x} = \frac 1 a \ln \size {\map \tan {\frac \pi 4 + \frac {a x} 2} } + C$

Also see

• Primitive of $\dfrac 1 {\sin a x}$

• Primitive of $\dfrac 1 {\tan a x}$

• Primitive of $\dfrac 1 {\cot a x}$

• Primitive of $\dfrac 1 {\sec a x}$

• Primitive of $\dfrac 1 {\csc a x}$