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Take a factor constant on each side of zero for an inverse times its derivative - #1919
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…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-each-side-of-zero
…n BREAKING-CHANGES 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 #718.
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1/sqrt(1 + b x^2),asin(sqrt(1 + b x^2))leaves a ratiosqrt(-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 assqrt(-b) ln(b asin(sqrt(1 + b x^2)))/b, which is wrong for every negative x: its derivative is the integrand timessgn(x). Master has declined it since then. The answer now carries the factorsqrt(-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):
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura