AQuotientOfDistinctSumsOverAPowerOfTheVariable​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

A power of the cotangent is (1/u)^k under the tangent, and over one bar it is
1^k above and u^k below: Rubi's 4.3.3.1
cot(c + d x)^7 (a + b tan(c + d x))^4 (A + B tan(c + d x)) is
1^7 (a + b u)^4 (A + B u)/(u^7 (1 + u^2)), which the simplifier spent 4.8 of the
integral's 5 GB on to hand back without the 1^7. The sums have constant terms, so
the power of u divides none of them and the quotient is in lowest terms as before. Only
with an exponent no other power below the bar has, since the gathering of neighbours to
one power was measured for sums alone.
https://github.com/asc-community/AngouriMath/issues/233