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Read a power of a power of a linear beside an exponential of a linear - #2105
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Rafael-SOWNet merged 1 commit intoOct 24, 2026
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((d + e x)^n)^m F^(c (a + b x)) is a gamma function of order n m + 1, with ((d + e x)^n)^m standing as written where (d + e x)^(n m) would: the two differ off the right half-line, but their logarithmic derivatives are both n m e/(d + e x), and that is all the answer asks of the power. The rule read only a power of the linear itself, so the integral was left unsolved. Part of #2075. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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October 24, 2026 20:26
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Part of #2075.
F^(c (a + b x)) ((d + e x)^n)^m(Rubi 2.1:30) was unsolved. It is a gamma function of ordern m + 1, and the power of a power stands as written where(d + e x)^(n m)would. The two differ off the right half-line, but both have the logarithmic derivativen m e/(d + e x), and that is all the answer asks of the power. The gamma rule read only a power of the linear itself; it now peels nested powers down to the linear.which is Rubi's form.
Corpus (the full fair Rubi corpus, at
647aa81aagainst master's composite at9cec2d5b): 49,010 → 49,025, none lost, 0 wrong. Fourteen of the fifteen (3.3:285–287, 5.1.2:157–160, 5.2.2:157–160, 5.1.5:260–262) are #2098's and #2100's, already on master, so this adds 2.1:30. Allocation per stream 1.0001 / 0.9999 / 1.0001. The suite passes; rebased ontoe1fe08c2.Tests:
APowerOfAPowerOfALinearinAPowerBesideAnExponentialOfAPowerIntegralTest, three integrands, each differentiated back.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura