[Rafael-SOWNet]

Part of #233.

Thirteen of Rubi's exponential, logarithmic and hyperbolic rows that master 6e16aae declines or runs out of time on:

• One shifted linear. A transcendental function of one shifted linear c + d x alone is written in u = c + d x, where a power of the linear stands below the bar inside a sum or the linear is written two ways: F^(a + b/(c + d x)^3)/(c + d x)^19, ln(c (d + k/(f + g x)^3)^q).
• Onto the exponential integral. Powers of two linears beside a negative power of a logarithm of their quotient are taken onto the exponential integral in that quotient. Separately, the zero-discriminant case of SolveAnExponentialOverSeveralLinears no longer divides by the difference of its two equal roots.
• Over a power of a logarithm or an inverse. The derivative of a function over a power of a logarithm, of an inverse trigonometric function, or of a sum holding a logarithm, whose terms are not elementary apart.
• Products of powers. A product of powers whose logarithmic derivative is a constant. A power with x in both base and exponent is read as an exponential, with the free terms of its exponent raised: x^(-2 - 1/x) (1 - ln(x)) is -(x^(-1/x))'. Master had since gained its own reading of x-in-both powers, and the rebase merged the two.
• Risch–Norman. The ansatz gains li(x), and erfi beside one Gaussian, in a second pass.

Scopes, found by the first chain's allocation check. Fifteen rows had grown past 1.3x, up to +5.5 GB, with the same answers.

• The Gaussian pass now runs only beside a factor of x alone below the bar, and only for one Gaussian. A polynomial times exponentials of a quadratic, or a hyperbolic function of one, is the job of the rules after it.
• The shifted-linear rule now reads only integrands of complexity 80 or less, as written. Its targets are 17 to 25, while the inverse sine's expansion of (d + e x^2)^3 (a + b asinh(c x))^2 cost 370 MB to read.

Chain against master 6e16aae, after the scopes:

• The pocket of 1,105 rows went from 1,072 to 1,085 solved, with 0 wrong.
• Family 3's sample went from 222 to 224; the others are unchanged.
• The 13 rows that moved, run alone, went from 0 to 13 solved.
• 6,603 rows were compared for allocation, and none grew past 1.3x.

The full unit suite passes locally: 16368 passed, 0 failed. The branch is rebased onto 47ab958, and the 13 still answer there. The BREAKING-CHANGES lengths were re-measured, and the v2.5.0 column was measured on a build: four rows that 2.5.0 runs past twenty seconds on now say so.

Rebased onto 2a98be4, after #2030. That entry's two 3.2.1 rows, 1/((a g + b g x)^2 (A + B ln(k (a + b x)/(c + d x)))^2) and its n-th-power twin, are now answered first by this branch's rule onto the exponential integral. They come back in 340 and 394 characters where #2030 wrote 358 and 412, and the commit updates those two rows of its entry.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura