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Integrate a power of a sum beside its derivative with symbolic powers in it - #1954
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Rafael-SOWNet merged 1 commit intoOct 19, 2026
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… in it c g' g^k is c g^(k + 1)/(k + 1), and c ln(g) for k = -1, but the derivative of ln(c x^n)^q is written q ln(c x^n)^(q - 1) c n x^(n - 1)/(c x^n), which nothing brought down to the n q ln(c x^n)^(q - 1)/x the integrand writes. The terms are now read as a coefficient times powers of x and of the other functions of x in them, each base's powers merged, and a power of x common to the sum's terms is taken out of it: a x^m + b x ln(c x^n)^q is x (a x^(m - 1) + b ln(c x^n)^q). Rubi's 3.5: rows 29, 31, 38, 39 and 40 go from unevaluated or timed out to solved (family 3 1349 -> 1354 of 1382), 0 wrong. Families 0 and 1 and samples of 2-8 otherwise identical; gate and suite pass. 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.
(a m x^m + b n q ln(c x^n)^(q - 1))/(x (a x^m + b ln(c x^n)^q))and four more of Rubi's 3.5 were declined. Each is a constant timesg' g^kfor a sumg, but the derivative ofln(c x^n)^qis writtenq ln(c x^n)^(q - 1) c n x^(n - 1)/(c x^n). Nothing brought that down to then q ln(c x^n)^(q - 1)/xthe integrand writes, andSolveALogarithmicDerivativeWithASymbolicExponentreads only powers ofx.The new rule,
SolveAPowerOfASumBesideItsDerivativeWithSymbolicPowers, reads each term as a coefficient times powers ofxand of the other functions ofxin it, with each base's powers merged. A power ofxcommon to the sum's terms is taken out of it, soa x^m + b x ln(c x^n)^qisx (a x^(m - 1) + b ln(c x^n)^q). It applies only where a power is symbolic; otherwise the substitution answers.Measured against master
8a1ef454:Rebased onto #1950–#1953 without conflict. All six rows were declined or timed out on 2.5.0, and
BREAKING-CHANGES.mdhas the entry.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura