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Integrate a polynomial beside a sine of a power of a shifted linear in that linear - #2095
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Rafael-SOWNet merged 1 commit intoOct 23, 2026
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…n that linear The rule that writes a polynomial beside a function of one shifted linear a + b x in u = a + b x took an exponential of a power of it and a power of a logarithm of it. It now takes a sine or a cosine of a sum that is not linear, in whatever holds it: x sin(a + b (c + d x)^n) and x (a + b sin(c + d (f + g x)^n))^2. In u these are powers of u beside the sine of a power of u, which Euler's formula writes as exponentials of that power, each a gamma function. Part of #2075. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Extends #2087's rule for a polynomial beside a function of one shifted linear to a sine or a cosine of a power of it. Part of #2075.
The rule. #2087 writes a polynomial beside a function of one shifted linear
a + b xinu = a + b x. It took an exponential of a power of the linear and a power of a logarithm of it. It now also takes a sine or a cosine of a sum that is not linear, in whatever holds it:x sin(a + b (c + d x)^n), andx (a + b sin(c + d (f + g x)^n))^2. Inuthese are powers ofubeside a sine of a power ofu. Euler's formula writes that as exponentials of the power, and each term is a gamma function (#2085).Measured on Rubi's suite, with the harness that reads
GAMMA, against68211405, the whole corpus each side. This branch was measured on2be40bad, which adds #2088 to that base, and is rebased onto master now.68211405The gains are 4.1.12's 13 rows, the last the file had. The other 5 are #2088's:
6.1.1:205-207and6.1.3:98/100. The new answers take 0.3 to 2.5 s each, against 11 to 125 ms for master to decline them. Time per stream is 1.030, 1.007 and 0.920 of the base's, and allocation 1.0002, 1.0002 and 0.9961. One row's allocation grew in the run,6.1.7:196, which is the same alone on both builds (1.079 GB), as it was for #2088, #2090 and #2093.Four integrals differentiate back in the tests. The suite passes (16,956), and so do the MCP tests (329).
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura