Primitive of Tangent of a x over x

Theorem

 * $\displaystyle \int \frac {\tan a x} x \ \mathrm d x = a x + \frac {\paren {a x}^3} 9 + \frac {2 \paren {a x}^5} {75} + \cdots + \frac {\paren {-1}^{n - 1} 2^{2 n} \paren {2^{2 n} - 1} B_{2 n} \paren {a x}^{2 n - 1} } {\paren {2 n - 1} \paren {2 n}!} + \cdots + C$

where $B_n$ denotes the $n$th Bernoulli number.

Also see

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


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


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


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


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