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Take a power of x out of the bracket of the derivative of a product of powers - #1916
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Rafael-SOWNet merged 4 commits intoOct 17, 2026
Merged
Rafael-SOWNet merged 4 commits into
Rafael-SOWNet merged 4 commits into
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…f powers A bracket that is a polynomial with a power of x in every term has that power taken out, to join the powers it multiplies: x^(2n) (c + d x)^n (2 c x + 3 d x^2) is x^(2n + 1) (c + d x)^n (2 c + 3 d x), the derivative of x^(2n + 2) (c + d x)^(n + 1)/(n + 1), and with the x in the bracket nothing raised x by enough. Rubi's 1.3.1 had it declined. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…en-out-of-the-bracket-of-a-derivative
…dard2.0 lacks Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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.
SolveAsTheDerivativeOfAProductOfPowersraises the powers an integrand already has and looks for a product whose derivative is the integrand. A bracket with a power of x in every term hid one of those powers:x^(2n) (c + d x)^n (2 c x + 3 d x^2)isx^(2n + 1) (c + d x)^n (2 c + 3 d x), the derivative ofx^(2n + 2) (c + d x)^(n + 1)/(n + 1). With the x still in the bracket, nothing raised x by enough.WithAPowerOfXOutOfTheBracketnow takes the lowest power of x out of every polynomial factor whose terms all hold one, and the rule reads the rebuilt integrand. Only the reading changes, so the answer is the same product it would have found had the integrand been written that way.Checks
APowerOfXOutOfTheBracketOfADerivativeIntegralTest: 2 cases, differentiated back at four points under two pin sets.KeyValuePair, and the second commit fixes that.Corpus, measured against master bf4be60 (this branch then merged f9c0ac1):
1.3.1:272 solves on this branch re-run alone, and does not on master. No losses and no slow rows. Gate passed; suite 15,483 passed, 0 failed.
Both cases were
integral(...)on 2.5.0 and are 61 and 65 characters here (BREAKING-CHANGES entry).🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura