Primitive of Secant of a x over x

Theorem

 * $\displaystyle \int \frac {\sec a x} x \ \mathrm d x = \ln \size x + \frac {\paren {a x}^2} 4 + \frac {5 \paren {a x}^4} {96} + \frac {61 \paren {a x}^6} {4320} + \cdots + \frac {\paren {-1}^n E_n \paren {a x}^{2 n} } {\paren {2 n} \paren {2 n}!} + \cdots + C$

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

Also see

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


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


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


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


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