Primitive of Tangent of a x over x

Theorem

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

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

Also see

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