TryReadAHomogeneousTrigonometricProduct​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​AngouriMath.​Entity@,​System.​Int32@,​AngouriMath.​Entity@)

Reading the whole product at once expands it first, and an expanded power is a
polynomial the rational integrator has to factor again: (a cos(x) + b sin(x))^4 became a^4 + 4 a^3 b t + 6 a^2 b^2 t^2 + 4 a b^3 t^3 + b^4 t^4 under
t = tan(x), which with numbers is (2 + 3t)^4 again in a moment and with
symbols is a quartic nothing factors -- sec(x)^2/(a cos(x) + b sin(x))^4 ran past
ten minutes where (1 + t^2)^2/(a + b t)^4 takes half a second. The whole product is
still read at once where a factor on its own is not homogeneous.