NEIM problem in @rule macro

[Bumblebee00]

neim stands for negative exponents in multiplications

If I define a rule with this pattern @rule ((~!a) + (~!b)*(~x))^(~m)*((~!c) + (~!d)*(~x))^(~n)~)) it can correctly match something like (1+2x)^2 * (3+4x)^3. But when one of the two exponents is negative, let's say -3, this expression is represented in julia as (1+2x)^2 / (3+4x)^3). Or when both are negative, the expression is represented as 1 / ( (1+2x)^2 * (3+4x)^3 ). The matcher inside the rule instad, searches for a *
as first operation, and thus doesn't recognize the expression.

here I have proposed a solution

A real word occurrence of this problem is that expressions like (1 + 3x)^2 / (1 + 2x)), (x^6) / (1 + 2(x^6)) and many others dont get integrated in the rule-based SymbolicIntegration.jl package.