[Rafael-SOWNet]

Part of #233.

• A power of x past the second beside a high power of a binomial in x², left to the binomial rules. SolveARationalFunctionOverAPowerOfASymbolicQuadratic already declined an odd integrand beside a power of x and a binomial in x^2 to the sixth power or past it, leaving it to the substitution in x^2. An even one is the binomial rules' x^m (a + b x^2)^p, but it was peeled here instead. Rubi's 1.1.2.2 1/(x^4 (a + b x^2)^10) had the power of x taken off four times, over ten levels of the recurrence each. It came back in 75,607 characters with its like terms never gathered, and was judged partial. Past the second power of x the rule now declines, and the binomial rules write 8,559 characters.

Integrand	master 78cd31b	this branch
1/(x^4 (a + b x^2)^10)	75,607 characters, 4.8 s, 0.58 GB	8,559 characters, 2.9 s, 0.55 GB
1/(x^6 (a + b x^2)^8)	33,638 characters, 1.2 s, 0.37 GB	6,063 characters, 0.5 s, 0.30 GB
1/(x^2 (a + b x^2)^10)	15,658 characters	unchanged

• Beside x² it is a trade, and it is left as it was. There the binomial rules are shorter but cost four times as much: 8,322 characters and 0.49 GB, against 15,658 and 0.10 GB. The first version of this branch declined there too, and the chain's allocation check flagged it.

Chain against master 78cd31b, before the narrowing to past x²:

• The pocket of 7,790 rows (every 1.1.2.* and 1.2.1.* file) went from 7,788 to 7,789 solved, with 0 wrong.
• Every family's sample is unchanged.
• The one row that moved, 1.1.2.2:236, went from partial to solved.
• 13,328 rows were compared for allocation. One grew past 1.3x and 300 MB: 1.1.2.2:235, the x² trade above, which the narrowing returns to master's answer.

The full unit suite passes locally on the narrowed version: 16,551 passed, 0 failed. The BREAKING-CHANGES lengths were measured on the branch. Rebased onto 37e2b1a.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura