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Gather powers of multiples of powers of one linear into one power - #1901
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Rafael-SOWNet merged 3 commits intoOct 16, 2026
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…ar into one power B^p for B = lambda L^k is (B^p/L^(k p)) L^(k p), and the quotient is constant wherever it is continuous, so it stays in front as written. Rubi's 1.1.1.2 1/(sqrt(-2 - b x) sqrt(2 + b x)), 1.1.1.3 (a + b x)^n/(x (-a - b x)^n) and 1.3.1 (a^3 + 3 a^2 b x + 3 a b^2 x^2 + b^3 x^3)^p were declined. Dispatched late, so the rules before it keep the shapes they answer. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…r-are-gathered-into-one-power # Conflicts: # Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Part of #718.
A power
B^pthat is not whole, of a polynomialBthat is a constant timesL^kfor one linearL, is(B^p/L^(k p)) L^(k p). The quotient's logarithmic derivative isp B'/B - k p L'/L = 0, so it is constant wherever it is continuous and stays in front as written.SolvePowersOfOneLinearAsOnePowergathers such powers by the root ofL, integrates the one power that results, and checks it by differentiating back.It is dispatched last of the rewrites, just before
SolveByScalingTheVariable. Asked first, it lengthened answers the rules before it already give:((a + b x)^3)^(1/3)came out in 111 characters where they write 25. A test pins that both stay with the earlier rules.Checks
npast the wrap at 2.3: 360/360.PowersOfOneLinearAsOnePowerIntegralTest: 6 cases.Corpus, measured against master 55a8044 (this branch then merged ded0d68):
Two family-3 rows timed out on the branch in the chain, 3.2.1:292 and 3.2.3:49. Re-run alone, both arms agree on both (one solved, one unsolved). The chain was sharing the machine. Gate passed; suite 15,419 passed, 0 failed.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura