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Keep the sign of a half-odd power of a negative multiple through the long division - #1957
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Rafael-SOWNet merged 1 commit intoOct 20, 2026
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…long division The polynomial reader took `(c x)^r` apart as `c^r x^r` for any constant c and a power r that is not whole. That holds for c > 0 and not for c < 0, where c x is positive and c^r and x^r are both imaginary. So `sqrt(-x) (x + 1)/x` was integrated as `2i sqrt(x)^3/3 + 2i sqrt(x)` and simplified to `i (sqrt(x) + x^(-1/2))`, each the negative of the right value for every x < 0, where the integrand is real. Such a power now comes apart over a positive number only. The limits at +oo read the variable as positive, and they say so to the reader. Answered as a result, with b under the power and right for either sign of b: - `(b x)^(5/2) (x^2 - 1)/x`; - Rubi's 4.3.0 `(b sec(x))^m tan(x)^3` and `cot(x)^3 (b csc(x))^m` at a half-odd m. 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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The polynomial reader took
(c x)^rapart asc^r x^rfor any constantcand a powerrthat is not whole. That holds forc > 0. Forc < 0,c xis positive wherex < 0, andc^randx^rare both imaginary there, so the answer comes out with the wrong sign. Such a power now comes apart over a positive number only. The limits at+ooread the variable as positive and tell the reader so.Wrong answers in 2.5.0, each the negative of the right value for every
x < 0, where the integrand is real:sqrt(-x)*(x+1)/x,Integrate2i * (sqrt(x)) ^ 3 / 3 + 2i * sqrt(x) + C(sqrt(-x) * x / (3/2) + sqrt(-x) / (1/2) provided not x = 0) + Csqrt(-x)*(x+1)/x,Simplifyi * (sqrt(x) + x ^ (-1/2))(-3*x)^(5/2)*(x+1)/x,Integrate(-3)^(5/2) x^(7/2)/(7/2) + …((-3) x)^(5/2) x/(7/2) + …Answered as a result, with
bunder the power and right for either sign ofb:(b x)^(5/2) (x^2 - 1)/x;(b sec(x))^m tan(x)^3andcot(x)^3 (b csc(x))^mat a half-oddm.Measured on
8a1ef454, branch against master:Two problems moved. Both time out on both builds when re-run alone, so they are load noise. No run had a wrong answer. Gate and suite (15,618) pass.
AHalfOddPowerOfANegativeMultipleIntegralTestchecks both signs ofband of the variable.BREAKING-CHANGES.mdhas the entry.Part of #233.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura