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Integrate a power of x times a hyperbolic function of a power under that power - #1971
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Rafael-SOWNet merged 1 commit intoOct 20, 2026
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…hat power x^m F(sinh(c + d x^n), cosh(c + d x^n)), with n >= 2 dividing m + 1, is taken under t = x^n: x^m dx is t^(k - 1) dt/n for k = (m + 1)/n, and the question in t is the same function of a linear in t beside a whole power of t, which the rules for those answer. The parser writes the hyperbolic functions as exponentials of c + d x^n, which the substitution search did not read as a function of x^n. Rubi's 6.1.3, 6.2.3, 6.5.2 and 6.6.2, seven rows with x sech(a + b x^2)^7 among them, were past the budget. Part of #233. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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x^m F(sinh(c + d x^n), cosh(c + d x^n)), withn >= 2dividingm + 1, is now taken undert = x^n. Therex^m dxist^(k - 1) dt/nwithk = (m + 1)/n, and the question intis the same function of a linear intbeside a whole power oft, which the rules for those answer. The parser writes the hyperbolic functions as exponentials ofc + d x^n, which the substitution search did not read as a function ofx^n.Measured on
8a1ef454, branch against master:Re-run alone on both builds, 7 problems go from timed out to answered, in 0.08–1.3 s: Rubi's 6.1.3:32, 6.2.3:32, 6.5.2:26/40, 6.6.2:26/40 and 6.7.1:1246. None goes the other way. No run had a wrong answer.
APowerOfXTimesAHyperbolicFunctionOfAPowerIntegralTestdifferentiates the answers back.BREAKING-CHANGES.mdhas the entry, with the 2.5.0 column measured on v2.5.0.Part of #233.
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