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Integrate an exponential of the reciprocal of a linear beside another linear - #1950
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… linear Under u = 1/(c + d x), a whole power of another linear p + q x is ((d p - q c) u + q)/d times c + d x, so the question in u is an exponential beside a rational function, which the exponential integral and the moments answer. The reader took only powers of c + d x itself, and a quotient N/L in the exponent with N linear is now read the same way. Rubi's 2.3: 25 rows go from unevaluated to solved (604 -> 629 of 650 in family 2), 0 wrong. Families 0 and 1 and samples of 2-8 otherwise identical; gate and suite pass. Part of #233. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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…in u = 1/(c + d x) first (#2010) #1950's SolveAnExponentialInTheReciprocalOfALinear answers these in a few megabytes, but sits near the end of the dispatcher, and the routes ahead of it spent seconds and gigabytes declining. Two early rules: SolveAnExponentialInTheReciprocalOfALinearOverAnotherLinear calls it right after SolveAGaussianInAReciprocal when the exponent is linear in u and a linear below the bar has a slope in u, d g - c h, that is not zero by value. SolveAnElementaryMomentOfAnExponentialInAPowerOfTheReciprocal answers F^(A + B/L^k)/L^n for k from 2 to 8 and n - 1 a positive multiple of k, the elementary cases, which w = u^k makes a polynomial times an exponential. The power below the bar reaches the dispatcher written monic, (c/d + x)^n, and the shared reader took c/d + x for another linear with a slope in u that is zero only by value; the rule decides that by value and asks the clean question itself. Neither rule's question can be its own integrand again. Probe, all 650 rows of family 2: 623 -> 627 answered (2.3:393, 394, 395, 478), none lost, no new wrong, total 188 s / 104 GB -> 89 s / 60 GB; two answers respelled (2.3:364 166 -> 74, 2.3:390 70 -> 74 characters). Chain pocket of 1,938 rows: 1,922 -> 1,925 solved, allocation over those solved on both 286.5 -> 219.9 GB; samples unchanged; 2.3:394 22.8 s / 22.4 GB -> 0.5 s, 2.3:395 timeout -> 60 ms alone. No row's allocation grew past 1.3x. Part of #233. Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura Co-authored-by: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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Part of #233.
f^(c/(a + b x)) x^2,F^(a + b/(c + d x))/(e + f x)^m,e^(e/(c + d x)^2) (a + b x)^mandF^(e + f (a + b x)/(c + d x))/(g + h x)^mwere declined. Underu = 1/(c + d x), a whole power of another linearp + q xis((d p - q c) u + q)/dtimesc + d x, so the question inuis an exponential beside a rational function. The exponential integral and the moments answer that.ReadAnExponentialInTheReciprocalOfALineartook only powers ofc + d xitself. It now also reads a quotientN/Lin the exponent withNlinear.Measured against master
8a1ef454:The new answers are 0.5–1.8 thousand characters. All 25 rows were also declined by 2.5.0, and
BREAKING-CHANGES.mdhas the entry.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura