Primitive of Inverse Hyperbolic Tangent of x over a over x

Theorem

 * $\displaystyle \int \frac {\tanh^{-1} \dfrac x a \ \mathrm d x} x = \sum_{k \mathop \ge 0} \frac 1 {\left({2 k + 1}\right)^2} \left({\frac x a}\right)^{2k + 1}$

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 $\dfrac {\operatorname{sech}^{-1} \frac x a} x$


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