[Rafael-SOWNet]

Part of #233.

Seven of Rubi's algebraic rows that master f7f2a7a declines or runs out of time on:

• A negative power of x beside a power of a binomial. For x^m (a + b x^n)^p R(x^n) with m <= -2, a multiple of the derivative of x^(m + 1) (a + b x^n)^(p + 1) takes the pole at zero out and raises the power of x by n. The rest is asked on its own. This answers 1.1.3.4's 1/(x^3 (1 - x^3)^(2/3) (1 + x^3)), and 1.1.2.2's 1/(x^6 (a + b x^2)^10) and its neighbours, where the partial fractions ran past the budget.
• A derivative's constant read at a point. A product of powers whose brackets are proportional at sampled points, but whose quotient cannot be shown free of x, has its constant read at x = 1. This answers 1.1.3.3:544.
• Roots inside a root. Euler's substitution, or the sum of two roots of linears, rationalises the roots inside a root. This answers 1.3.2's sqrt(1 - x^2 + x sqrt(x^2 - 1)) and sqrt(-x + sqrt(x) sqrt(1 + x))/sqrt(1 + x), which Rubi itself does not integrate.

Two scopes, found by the first chain's allocation check.

• The raising rule declines where m + 1 is a multiple of n beside a root. There the substitution reads the integrand whole, and the rule asked what was left, declined it, and spent 22 GB before master's identical answer. That was 1/(x^5 (1 - x^2)^(1/3) (3 + x^2)^2): 5.75 GB on master, 27 GB before the scope.
• The nested-root rule takes only integrands that are roots and nothing else, with radicands that are polynomials in x and those roots. Under the tangent's substitution, (1 + coth(x))^(7/2) became a power of (u + 1)/u + sqrt(1 - u^2)/u, and the rule answered it in 1,661 characters where the rules after it give 287.

Chain against master f7f2a7a, after both scopes:

• The pocket of 814 rows went from 772 to 779 solved, with 0 wrong.
• The samples are unchanged.
• The 7 rows that moved, run alone, went from 0 to 7 solved.
• 6,304 rows were compared for allocation, and none grew by more than 23 MB.

The full unit suite passes locally: 16296 passed, 0 failed. Before the scopes it failed two coth tests, the same respelling. The BREAKING-CHANGES lengths were re-measured on the branch, and the v2.5.0 column on a v2.5.0 build.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura