Primitive of Secant of a x

Theorem

Tangent Form

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

where $\map \tan {\dfrac \pi 4 + \dfrac {a x} 2} \ne 0$.

Secant plus Tangent Form

$\ds \int \sec a x \rd x = \frac 1 a \ln \size {\sec a x + \tan a x} + C$

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

Also see

• Primitive of $\csc a x$