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Integrate a polynomial beside error functions of a shifted linear - #1947
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Rafael-SOWNet merged 1 commit intoOct 19, 2026
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Writes x^n erf(a + b x)^2 and its erfc and erfi kin in u = a + b x, where the unshifted rules already answer. By parts in x leaves a Gaussian of the shifted linear beside a polynomial, which nothing reads. Part of #1945. 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 #1945. Part of #1501.
(c + d x)^m erf(a + b x)^2, and the erfc and erfi forms, are now integrated by writing them in u = a + b x, where the unshifted rules already answer. Integrating by parts in x leavesx^n e^(-(a + b x)^2) erf(a + b x), which no rule handles. The rule only fires when every error function in the product has the same argument.Measured on master 4e5ae5f:
x erf(a + b x)^2integral(…), 2.4 sx^2 erf(a + b x)^2integral(…), 2.4 s(c + d x)^2 erf(a + b x)^2, and with erfc and erfix erf(b x) erf(a + b x)integral(…)The new answers check out exactly at 4 points, at 50, 300 and 2000 digits, with a, b, c, d = 13/10, 7/10, 19/10, 17/10.
Rubi checks, against master, with no wrong answers anywhere:
2.5.0 has no erf integration, so no answer changes and there is no BREAKING-CHANGES entry.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura