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Integrate a power of x beside a binomial in an odd negative power of x on both sides of 0 - #2038
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Rafael-SOWNet merged 1 commit intoOct 22, 2026
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…x on both sides of 0 SolveByTakingAPowerOfXOutOfAFractionalPower took x^(j p) out of a sum of whole powers of x under a fractional power p: for sqrt(a + b/x^3)/x it wrote x^(-3/2) sqrt(a x^3 + b), which has no value at a negative x, where a + b/x^3 is real, and fourteen of Rubi's 1.1.3.2 x^m (a + b/x^3)^(k/2) were answered for a positive x only. Past an odd j other than 1 and -1, where j p is not whole, the rule now declines, and the substitution in the root answers them on both sides: sqrt(a + b/x^3)/x is a function of u = sqrt(a + b/x^3). Where j p is whole, x^(j p) is real on both sides and the rule is kept: (a x^3 + b x^6)^(5/3), Rubi's 1.2.3.2, is x^5 times a power of a + b x^3. Chain against master 2a98be4: the 14 partial answers of 1.1.3.2 are solved on both sides, and the first version's guard, on the odd power alone, lost 1.2.3.2:8; keyed on j p it is answered again, 15 of 15 alone in the probe. 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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Part of #233.
SolveByTakingAPowerOfXOutOfAFractionalPowertakesx^(j p)out of a sum of whole powers of x under a fractional power p. Forsqrt(a + b/x^3)/xit wrotex^(-3/2) sqrt(a x^3 + b), which has no value at a negative x, wherea + b/x^3is real. So fourteen of Rubi's 1.1.3.2x^m (a + b/x^3)^(k/2)were answered for a positive x only. Past an odd j other than 1 and -1, wherej pis not whole, the rule now declines. The substitution in the root answers them on both sides:sqrt(a + b/x^3)/xis a function ofu = sqrt(a + b/x^3).j pis whole, the rule is kept. Therex^(j p)is real on both sides:(a x^3 + b x^6)^(5/3), Rubi's 1.2.3.2, isx^5times a power ofa + b x^3. The first version of the guard keyed on the odd power alone and lost that row. A test pins it now.Chain against master 2a98be4:
The full unit suite passes locally: 16,462 passed, 0 failed. The BREAKING-CHANGES lengths were measured on the branch. Rebased onto 78cd31b, keeping both entries where the BREAKING-CHANGES anchors met.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura