Primitive of Inverse Hyperbolic Tangent of x over a over x

Theorem

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

Also see

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


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


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


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


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