By analogy with the tanc function, define the tanhc function by
(1)

It has derivative
(2)

The indefinite integral can apparently not be done in closed form in terms of conventionally defined functions.
It has maximum at , and positive inflection point at the solution to
(3)

which is 0.919937667... (OEIS A133919).
It has a unique real fixed point at 0.82242927726... (OEIS A133918).