Repository navigation
Integrate an arctangent over a power of d (1 ± i c x) under the tangent - #1918
Merged
Rafael-SOWNet merged 3 commits intoOct 17, 2026
Merged
Rafael-SOWNet merged 3 commits into
Rafael-SOWNet merged 3 commits into
Conversation
Under x = tan(u)/c, 1 + i tan(u) is e^(i u)/cos(u), so x^m (a + b atan(c x))^p/(d (1 +- i c x))^k is (a + b u)^p (tan(u)/c)^m d^(-k) e^(-+i k u) cos(u)^(k - 2)/c, a polynomial in u times exponentials and trigonometric functions. Rubi's 5.3.4 (a + b atan(c x))^2/(d + i c d x)^2 and seven like it ran out of time. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…a-power-of-one-plus-i-c-x-under-the-tangent # Conflicts: # Sources/AngouriMath/Functions/Continuous/Integration/Integration.Definition.cs
…KING-CHANGES Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Part of #718.
Under
x = tan(u)/c,1 + i tan(u)ise^(i u)/cos(u). Sox^m (a + b atan(c x))^p/(d (1 ± i c x))^kbecomes(a + b u)^p (tan(u)/c)^m d^(-k) e^(∓i k u) cos(u)^(k - 2)/c, a polynomial inutimes exponentials and trigonometric functions. The new rule is asked early, ahead of the rules that spent the budget.Rubi chain (master arm at 1e79b0e, 5 s budget):
1/((a g+b g x)^2 (A+B log(...))^2), which takes 23 s on both arms when run alone, so it is noise.Gained on 2.5.0: eight rows of 5.3.4 that were all
integral(...). The branch answers them in 267 to 1,202 characters, each in under half a second.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura