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Integrate a whole power of the square of a polynomial over its root - #1898
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Rafael-SOWNet merged 3 commits intoOct 16, 2026
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Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…square-is-written-over-its-root # 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 whole power
P^nof a polynomial with symbols in it, wherePis the square of a polynomialR, is integrated asR^(2n), so(a^2 + 2 a b x^2 + b^2 x^4)^2is read as(a + b x^2)^4. The rules for a power of a binomial read the root, and the partial fractions took the trinomial whole. The rewrite holds whatever the signs, because the power is whole, and the answer is checked by differentiating it back. With numbers for coefficients the partial fractions already answer, so those are left alone.Rubi corpus, against master 7e5768b (both arms built and run in one chain; master then moved to d05d20d, merged here):
The six are 1.2.2.2:788–790 and 806–808, which time out on master and answer in about 50 ms here. Over all 734 corpus rows with such a trinomial, master solves 728 and this branch solves all 734, with nothing slower. There are no wrong answers. The performance gate and the unit suite (15,402 passed) pass. The exact check at 50–2,000 digits agrees on all six at three sign patterns of
aandb, 216/216.BREAKING-CHANGES.mdhas an entry for the six, measured on 2.5.0 and on this branch.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura