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

Powers of two linears beside a power of A + B ln(K (L1/L2)^n) in the same
two linears, by the substitution t = L1/L2: with L1 = a + b x and
L2 = c + d x, L1 = D t/(b - d t), L2 = D/(b - d t) and
dx = D dt/(b - d t)^2 for D = b c - a d, so the integrand is a power
of t times a power of b - d t times a power of A + B ln(K t^n),
which the rule above answers as a rational function beside a logarithm of
t. Rubi's (f + g x)^m (h + i x)^q (A + B ln(e ((a + b x)/(c + d x))^n))^p with f + g x and h + i x proportional to the log's linears, which
the rule above takes step by step and the substitution search spent its budget on:
(A + B ln(e (a + b x)/(c + d x)))/((a g + b g x)^2 (c j + d j x)^2) is
(A + B ln(e t))(b - d t)^2/(g^2 j^2 D^3 t^2), which answers at once. The
exponents may be symbols; (g L1)^m is taken as g^m L1^m and
K L1^n/L2^n as K t^n, the generic case, and the answer is checked
against the integrand at sampled points before it is given.