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Integrate a product of powers of a sine and a cosine beside a non-polynomial by linearising it - #1924
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Rafael-SOWNet merged 4 commits intoOct 17, 2026
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…ynomial by linearising it Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…d2.0 lacks Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…-of-a-sine-and-a-cosine-linearised # Conflicts: # Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs
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.
sin(u)^p cos(u)^qbeside a non-polynomial factor is written, by product-to-sum, as a sum of sines and cosines of multiples ofu. Each term is then a question the integrator already answers. The rule is asked late, afterSolveARationalFunctionTimesALogarithmOfPowersOfLinears(…, besideAPolynomialToo: true), so it only meets what the earlier rules have declined. It answers Rubi's 5.1.4x^3 (1 - c^2 x^2)^(5/2)/(a + b asin(c x))and its square, which underx = sin(u)/cbecome exactly this shape.Rubi chain (master arm at 67d8e8d, 5 s budget):
On 2.5.0 both rows were
integral(...). The branch answers them in 508 and 1,470 characters, each in about 0.6 s.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura