Primitive of Inverse Hyperbolic Tangent of x over a over x

Theorem

 * $\ds \int \frac {\tanh^{-1} \dfrac x a \rd x} x = \sum_{k \mathop \ge 0} \frac 1 {\paren {2 k + 1}^2} \paren {\frac x a}^{2 k + 1}$

Also see

 * Primitive of $\dfrac {\sinh^{-1} \frac x a} x$


 * Primitive of $\dfrac {\cosh^{-1} \frac x a} x$


 * Primitive of $\dfrac {\coth^{-1} \frac x a} x$


 * Primitive of $\dfrac {\sech^{-1} \frac x a} x$


 * Primitive of $\dfrac {\csch^{-1} \frac x a} x$