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A secant or a cosecant beside a power of a sum of them is read as a power of the cosine or the sine - #1857
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Rafael-SOWNet merged 3 commits intoOct 12, 2026
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Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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October 12, 2026 07:14
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Part of #718.
sec(x) sqrt(sec(x) + tan(x))was declined, with the rest of Rubi's 4.7.7 that puts a secant or a cosecant beside a power ofsec ± tanorcsc ± cot. Two reads were missing:SolveAsTheDerivativeOfAProductOfPowerstooksec(x)as a function of its own, notcos(x)^(-1), so the integrand was never seen as(sec + tan)'-shaped. A secant or cosecant factor, or a constant power of one, is now read as the reciprocal power of the cosine or sine.SolveByTangentSubstitutionwrote an odd power of the secant throughsqrt(1 + t^2)but not one of the cosecant, sosqrt(1 + tan(x)) csc(x) sec(x)stayed inx.sec(x)*sqrt(sec(x) + tan(x))2 * sqrt(sec(x) + tan(x))sec(x)*sqrt(sec(x) - tan(x))(-2) * sqrt(sec(x) - tan(x))csc(x)*sqrt(csc(x) + cot(x))(-2) * sqrt(csc(x) + cotan(x))sec(a + b*x)*(sec(a + b*x) + tan(a + b*x))^c1 / (b * c) * (sec(a + b * x) + tan(a + b * x)) ^ csqrt(1 + tan(x))*csc(x)*sec(x)Rubi corpus, branch against master b3805f8: one problem gained (4.7.7 #1125), none lost, 0 wrong in every family; the family-4 pocket gained two. Kernel gate and the full suite (15249 passed) pass.
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