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Integrate a polynomial times powers of polynomials by raising each power by one - #1968
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Rafael-SOWNet merged 1 commit intoOct 20, 2026
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…wer by one P R_1^(s_1) ... R_m^(s_m), with an exponent that is a fraction or a symbol, is answered as Q R_1^(s_1 + 1) ... R_m^(s_m + 1) for a polynomial Q where there is one. With R = R_1 ... R_m, the derivative of that is the integrand's powers times Q' R + Q sum_i (s_i + 1) R_i' R/R_i, and setting it equal to P is a linear system in the coefficients of Q. Rubi's (a g + e x - b g x^4)/(a + b x^4)^(3/2) is (2 a g x + e x^2)/(2 a sqrt(a + b x^4)), and 25 more of Rubi's 1.1.x and 1.2.x of that shape were declined or ran past the budget. A symbolic power of a constant multiple of x, (c x)^t, is read as such beside it. 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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P R_1^(s_1) ... R_m^(s_m), with an exponent that is a fraction or a symbol, is answered asQ R_1^(s_1 + 1) ... R_m^(s_m + 1)for a polynomialQ, where there is one. WithR = R_1 ... R_m, the derivative of that is the integrand's powers timesQ' R + Q sum_i (s_i + 1) R_i' R/R_i. Setting it equal toPis a linear system in the coefficients ofQ; where the system has no solution, the rule declines.For example, Rubi's
(a g + e x - b g x^4)/(a + b x^4)^(3/2)is(2 a g x + e x^2)/(2 a sqrt(a + b x^4)). A symbolic power of a constant multiple of x,(c x)^t, is read as such beside it.Measured on
8a1ef454, branch against master:Re-run alone on both builds, all 28 problems that moved answer on the branch, against 2 on master: 26 gained, across 1.1.1.3, 1.1.2.3, 1.1.3.2, 1.1.3.8, 1.2.1.3, 1.2.1.9, 1.2.2.5 and 1.2.3.5. None goes the other way. No run had a wrong answer.
APolynomialTimesPowersOfPolynomialsByRaisingThePowersIntegralTestdifferentiates the answers back.BREAKING-CHANGES.mdhas the entry, with the 2.5.0 column measured on v2.5.0.Part of #233.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura