Primitive of Secant of a x over x

Theorem

 * $\displaystyle \int \frac {\sec a x} x \ \mathrm d x = \ln \left\vert{x}\right\vert + \frac {\left({a x}\right)^2} 4 + \frac {5 \left({a x}\right)^4} {96} + \frac {61 \left({a x}\right)^6} {4320} + \cdots + \frac {E_n \left({a x}\right)^{2 n} } {\left({2 n}\right) \left({2 n}\right)!} + \cdots + C$

where $E_n$ is the $n$th Euler number.

Also see

 * Primitive of $\dfrac {\csc a x} x$