[Rafael-SOWNet]

Part of #233.

• An even quotient over a power of a biquadratic beside another factor, split in w = x^2. Rubi's 6.1.7 csch(c + d x)/(a - b sinh(c + d x)^4)^2 ran past the corpus's budget. Under w = cosh(c + d x) it is 1/((w^2 - 1)(a - b (w^2 - 1)^2)^2). Partial fractions in x split off the linears of x^2 - 1 and ran the series at their roots over the rest. Its coefficients came to a hundred thousand nodes, with powers like c^40 f^58.
• The change. In w = x^2 the integrand is 1/((w - 1) Q(w)^2). The split over written factors takes that with a repeated quadratic, and every term is a shape the rules answer at once. SolveAnEvenQuotientOverAPowerOfABiquadraticBesideAnotherFactorInTheSquare splits it so and asks each term in x. While the split is solved, each factor is made monic and its compound coefficients are named. Without naming, a - b (w - 1)^2 took 3 s and 1.4 GB; with it, 0.1 s.
• Where it applies. Only over a power of a biquadratic with all three terms. Over a power of a + b x^4 the split in x answers at once and in fewer characters. Every other factor must stand once, and the numerator must not vanish at a linear's root. A split past 20,000 nodes declines. The answer is checked by its derivative.
• The first chain lost eight rows, and that is what the guards are for. Under the tangent, sinh(u)^4/(a - b sinh(u)^4)^2 is w^2 (w - 1)^4/((1 - w)^3 Q^2). Split as written, that was 1.46 million nodes after 22 s. And the numerator's integers had been named, which hid the (w - 1)^6 they make. Each coefficient is now folded before it is named.

Input	master ef4150e	this branch
6.1.7:285 csch(c + d x)/(a - b sinh(c + d x)^4)^2	past the budget	2,511 characters, 0.07 s
1/((x^2 - 1)(c + d x^2 + f x^4)^2)	past 30 s	2,164 characters, 0.09 s
x^2/((x^2 + 1)(c + d x^2 + f x^4)^2)	13,714 characters, 3.8 s, 4.2 GB	2,062 characters, 0.08 s
1.2.2.3:381 1/((d + e x^2)(a + b x^2 + c x^4)^2)	18,154 characters, 10.9 s, 10.8 GB	9,968 characters, 0.9 s, 0.12 GB
the eight 6.1.7 rows sinh(u)^k/(a - b sinh(u)^4)^n	answered	the same answers, character for character

Chain against master ef4150e, re-run after the guards:

• The pocket of 3,547 rows went from 3,546 to 3,547 solved. It held every 1.2.2 row, 1.1.3.3, .4 and .6, and 4.1.7, 4.2.7, 6.1.7 and 6.2.7.
• Every family's sample is unchanged.
• The one row that moved is 6.1.7:285, run alone: a timeout on master, solved here.
• 9,151 rows were compared for allocation, and none grew past 1.3x and 300 MB.

The library builds for netstandard2.0, net8.0 and net10.0. The suite is left to CI. The BREAKING-CHANGES lengths were measured on the branch, and the 2.5.0 column on a v2.5.0 build. Rebased onto e30f63f.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

[Rafael-SOWNet]

Added 1.2.2.3:381 1/((d + e x^2)(a + b x^2 + c x^4)^2) to the table and to the BREAKING-CHANGES entry (1a834a5). It is solved on both sides, so the chain's verdict comparison did not list it. Alone, master answers it in 10.9 s and 10.8 GB with 18,154 characters, and this branch in 0.9 s and 0.12 GB with 9,968.