[Rafael-SOWNet]

Part of #233.

• A logarithm of nested powers of one linear, named as a multiple of the linear's logarithm. Rubi's 3.3 (g + h x)^2 (a + b ln(c (d (e + f x)^p)^q))^3 was declined after eleven seconds and twelve gigabytes. With ln(c (e + f x)^n) for the logarithm, the same integrand is answered in a quarter of a second.
• The change. The logarithm's derivative is p q f/(e + f x) by the chain rule on any branch, read off the nested powers as written. So it is p q ln(e + f x) + K, with K constant wherever it is continuous. That is the generic case, as SolveByNamingALogarithmLinearInTheVariable writes it. SolveByNamingALogarithmOfNestedPowersOfALinear names it so, and the integrand becomes a polynomial times a power of ln(e + f x). In the answer, the sum the name stands for is written back as the logarithm, so it reads (a + b ln(c (d (e + f x)^p)^q))^3 ... and not p q ln(e + f x) + (ln(...) - p q ln(e + f x)). It applies only to a nested power, which the rules for ln(c L^n) do not read.

Input (k for Rubi's e)	master ef4150e	this branch
3.3:620 (g + h x)^2 (a + b ln(c (d (k + f x)^p)^q))^3	declined, 11.5 s, 12.3 GB	1,660 characters, 1.2 s, 0.3 GB
(g + h x)^2 (a + b ln(c (d (k + f x)^p)^q))^2	2,048 characters	1,051 characters
(g + h x) (a + b ln(c (d (k + f x)^p)^q))^3	2,569 characters	702 characters
(g + h x)^2 (a + b ln(c (d (k + f x)^p)^q))	527 characters	631 characters

Chain against master ef4150e:

• The pocket of 1,382 rows, all of family 3 and every row with a nested power in a logarithm, went from 1,381 to 1,382 solved.
• Every family's sample is unchanged.
• The one row that moved is 3.3:620, run alone: declined on master, solved here.
• 6,986 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 de11aaf.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

[Rafael-SOWNet]

Rebased onto 7d1081e (#2048). There was one conflict in IndefiniteIntegralSolver.cs, where #2048's rule went in at the same place. Both rules are kept, #2048's first. The library builds for netstandard2.0, net8.0 and net10.0, and both rules' tests pass together, 7 of 7.

[Rafael-SOWNet]

Rebased onto 1566841 (#2054). The same conflict came back in IndefiniteIntegralSolver.cs, where #2054's rule went in at the same place. All three rules are kept. The library builds for every target, and the three rules' tests pass together, 8 of 8.