The scaling rule does not simplify an integrand with the imaginary unit in it

[Rafael-SOWNet]

Part of #718.

The rule that scales the variable by the integrand's one symbol simplified the scaled integrand three times, to separate the whole power of the scale it is homogeneous of. With the imaginary unit beside the symbol that search ran past any budget:

integrand	master 3a3d0163	this
((1 + i a x)/(1 - i a x))^(-5/4)/x^2	no verdict within 150 s	declined in 3.5 s
sec(c + d x)^3/(a + i a tan(c + d x))	no verdict within 150 s	3.8 s
x^4 e^(2 i arctan(a + b x))	83 s	16 s
1/(e^(3 i arctan(a + b x)) x^4)	declined after 41 s	declined in 18 s

Measured one integrand at a time on a loaded machine, so the last two are rough; the first two are not.

What changes. With the imaginary unit in the integrand, the scaled integrand is inner-simplified, which separates what a whole power of the scale does, and where the parts do not separate the rule declines at once. Without the imaginary unit nothing changes.

Tests: ComplexCoefficientRationalIntegralTest.AnImaginaryMobiusPowerIsDeclinedWithinAMinute: ((1 + i a x)/(1 - i a x))^(-5/4)/x^2 comes back within a minute, declined, where master ran past two.

Measured first on the 1,112 problems with the imaginary unit in them, at the corpus's 5-second budget, against master 97c4b692, the branch's base:

	master	this
solved	802	809
wrong	0	0

Measured then on the Rubi corpus against master 97c4b692:

	master	this
family 0, independent suites (1814)	1766	1766
family 1, 40 a file (1381)	1289	1288
families 2 to 8, sampled (2410)	2212	2212

No answer is wrong on either build. The 15 problems the two builds disagreed on, run again one build at a time, all ran out of time on master; here 9 are answered -- sec(c + d x)^2/(a + i a tan(c + d x)) and its cube, tan(c + d x)^(8/3)/(a + i a tan(c + d x)), 1/(a + b csc(c + d x)^2)^4, and five powers of x beside e^(k i arctan(a + b x)) -- 5 are declined in seconds, and one, from 1.1.1.5 and the change in family 1, runs out of time on both.

The suite passes on the commit measured, 9e190e5b, 14,586 tests, and so does the allocation gate. Master 3a3d0163 is merged in since, without conflicts, after a commit with the entry in BREAKING-CHANGES.md that the corpus showed this owes. The calculus tests pass on the merge, 3,960 of 3,961; the other, a 30-second wall clock on declining sin(x)/(x^3 + 1)^2, failed under the machine's load and passes on its own, and that integral is declined in 1.4 s on both builds.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura