Primitive of Inverse Hyperbolic Cotangent of x over a over x

Theorem

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

Also see

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


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


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


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


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