[Rafael-SOWNet]

Part of #233.

• An inverse sine of a sine of a linear, named as linear on each interval. Rubi's 5.1.5 x/asin(sin(x)) was declined. On each interval where cos(L) keeps its sign, asin(sin(L)) for L = a + k x is s k x + c, with s = cos(L)/sqrt(cos(L)^2) and c constant there. acos(cos(L)) is the same with the sign of sin(L).
• The change. SolveByNamingAnInverseSineOfASineLinearOnEachInterval names the inverse sine so, with s and c as symbols. The integrand is then a rational function of x. Its answer is written back, using s^2 = 1: a whole power of s is 1 or s, and a division by s is a multiplication. A sum equal to s k x + c is the inverse sine again, decided in lowest terms over the symbols, so the logarithm holds asin(sin(x)) and not s x + (asin(sin(x)) - s x). The answer is the generic case's on every interval, as SolveByNamingALogarithmLinearInTheVariable's is.
• Dispatched last, so a polynomial beside the inverse sine keeps the answer parts already gives it.
• 2.5.0 answered 1/asin(sin(x)) wrongly, as ln(asin(sin(x))), which is wrong wherever cos(x) < 0. Master declined it before this change. The BREAKING-CHANGES entry records both.

Input	master ef4150e	this branch
5.1.5:619 x/asin(sin(x))	declined	111 characters
1/asin(sin(x))	declined	50 characters, ln(asin(sin(x))) cos(x)/sqrt(cos(x)^2)
asin(sin(x))/x	declined	222 characters
x/acos(cos(a + b x))	declined, 2.0 s	171 characters, 0.25 s

Each is checked at -2.3, -0.9, 0.4, 1.3, 2.2 and 2.9, on both sides of a zero of the cosine.

Chain against master ef4150e:

• The pocket of every 5.1 and 5.2 row, 773 of them, went from 772 to 773 solved.
• Every family's sample is unchanged.
• The one row that moved is 5.1.5:619, run alone: declined on master, solved here.
• 6,377 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.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

[Rafael-SOWNet]

Rebased onto e006a79 (#2045) with one conflict in BREAKING-CHANGES.md, two entries at one anchor; both kept, #2045's first. The library builds for netstandard2.0, net8.0 and net10.0.