Skip to content

Read a power of a power of a linear beside an exponential of a linear - #2105

Merged
Rafael-SOWNet merged 1 commit into
masterfrom
a-power-of-a-power-of-a-linear-beside-an-exponential
Oct 24, 2026
Merged

Rafael-SOWNet merged 1 commit into
masterfrom
a-power-of-a-power-of-a-linear-beside-an-exponential

Conversation

@Rafael-SOWNet

Copy link
Copy Markdown
Member

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 order n 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 derivative n 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.

integrate(F^(c*(a+b*x))*((d+e*x)^n)^m)
  = F^(a c - b c d/e) ((d + e x)^n)^m (-ln(F) b c (d + e x)/e)^(-n m) gamma(n m + 1, -ln(F) b c (d + e x)/e)/(ln(F) b c)

which is Rubi's form.

Corpus (the full fair Rubi corpus, at 647aa81a against master's composite at 9cec2d5b): 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 onto e1fe08c2.

Tests: APowerOfAPowerOfALinear in APowerBesideAnExponentialOfAPowerIntegralTest, three integrands, each differentiated back.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

((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
@Rafael-SOWNet Rafael-SOWNet added this to the 2.7.0 milestone Oct 24, 2026
@Rafael-SOWNet
Rafael-SOWNet merged commit 191510f into master Oct 24, 2026
34 checks passed
@github-project-automation github-project-automation Bot moved this from Todo to Done in AngouriMath Oct 24, 2026
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

Status: Done

Development

Successfully merging this pull request may close these issues.

1 participant