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Take a factor constant on each side of zero for an inverse times its derivative - #1919

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a-factor-constant-on-each-side-of-zero
Oct 17, 2026
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Rafael-SOWNet merged 3 commits into
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a-factor-constant-on-each-side-of-zero

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Part of #718.

Next to 1/sqrt(1 + b x^2), asin(sqrt(1 + b x^2)) leaves a ratio sqrt(-b x^2)/(b x) to its derivative. That ratio is constant while x keeps its sign and changes sign across 0. It was compared with its value at 3/10, so the check failed at the negative points and the integral was declined. Now each side of 0 is compared with that side's own value.

On 2.5.0, 1/(asin(sqrt(1 + b x^2)) sqrt(1 + b x^2)) was answered as sqrt(-b) ln(b asin(sqrt(1 + b x^2)))/b, which is wrong for every negative x: its derivative is the integrand times sgn(x). Master has declined it since then. The answer now carries the factor sqrt(-b x^2)/(b x) and holds on both sides. There is a BREAKING-CHANGES entry.

Rubi chain (master arm at 1e79b0e, 5 s budget):

  • Pocket of 1,774 rows: this branch solves 1,707, master 1,703.
  • Families 0–8 sampled: identical on both arms.
  • Moved rows run alone: the branch solves 4 of 4, master 0. These are 5.1.5:620 and 621 and 5.2.5:190 and 191, the arcsine forms and their arccosine twins.
  • Gate: passed.
  • Suite: the chain's suite run was killed by my local memory guard at 8.2 GB. The full suite on the master arm (1e79b0e) is killed the same way, at the same point, so the spike was already on master and this branch did not cause it. The Calculus tests alone and every other test alone both pass on this branch (4,684 and 10,809 passed). CI runs the full suite.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

Rafael-SOWNet and others added 3 commits October 16, 2026 22:06
…derivative

asin(sqrt(1 + b x^2)) beside 1/sqrt(1 + b x^2) leaves sqrt(-b x^2)/(b x), constant where x keeps its
sign and changing with it; compared with its value at 3/10 it failed at the negative points and the
integral was declined. It is compared on each side of 0 with that side's value now. Rubi's 5.1.5
asin(sqrt(1 + b x^2))^n/sqrt(1 + b x^2) and 5.2.5's arccosine twins, four rows, were declined.

Part of #718

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…n BREAKING-CHANGES

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 2.6.0 milestone Oct 17, 2026
@Rafael-SOWNet
Rafael-SOWNet merged commit 03b1aa7 into master Oct 17, 2026
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@github-project-automation github-project-automation Bot moved this from Todo to Done in AngouriMath Oct 17, 2026
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