SolveByNamingALogarithmLinearInTheVariable​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean)

A logarithm of x whose derivative in x is a
constant k is k x + c for a constant c, and is written so, with
c a name standing for ln(...) - k x, which the answer substitutes back.
ln(e^(2(a + b x))) -- which is what atanh(tanh(a + b x)) is once its
quotient is cancelled -- has derivative 2b, and is 2b x + c: with that
name, x^m atanh(tanh(a + b x))^3 is a polynomial times a power of a linear and
1/(x atanh(tanh(a + b x))) a rational function, which the rules answer at once
where the logarithm was an atom no rule read past the first power. The name is
exact: c is ln(...) - k x by definition, and a constant in x because the derivative is. The logarithm is not unwrapped to its argument's
exponent, which it equals only on a strip; Rubi's answers carry
b x - atanh(tanh(a + b x)) in the same way. Rubi's 7.3.7 and 7.4.1. Asked as
a question of its own. https://github.com/asc-community/AngouriMath/issues/718