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Integrate a power of x beside powers of a quotient of linears and of their product as one term, and 1/(a + b asinh(±i + d x^2))^n - #2032
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Rafael-SOWNet merged 1 commit intoOct 21, 2026
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…their product as one term, and 1/(a + b asinh(+-i + d x^2))^n - x^j T^alpha Q^beta, for T = (1 + a x)/(1 - a x) and Q = c - a^2 c x^2, as T^alpha Q^(beta + 1) times a polynomial of degree j - 1, found by one linear solve whose last equation is checked; where it fails the rule declines. Rubi's 7.3.6, e^(n artanh(a x)) x^2 (c - a^2 c x^2)^p, the parser having folded the exponential into T^(n/2). - The six of Rubi's 7.1.5 1/(a + b asinh(+-i + d x^2))^n by the rule for the inverse hyperbolic sine of a quadratic, with g = cosh(u/2 + c pi/4): cosh(u/2) + c sinh(u/2) is sqrt(2) times it, and its square is 1 + c sinh(u) = c d x^2. They are complex at every x, and checked there. Chain against master f7f2a7a: pocket of 2,374 rows, 2,362 -> 2,372 solved, 0 wrong; family 7's sample 269 -> 270, the others unchanged; the 10 rows that moved, alone, 0 -> 10 solved; 7,894 rows compared for allocation, none grew past 109 MB. 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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Part of #233.
T = (1 + a x)/(1 - a x)andQ = c - a^2 c x^2,x^j T^alpha Q^betais integrated asT^alpha Q^(beta + 1)times a polynomial of degreej - 1. The polynomial is found by one linear solve whose last equation is checked; where that equation fails, the rule declines. These are Rubi's 7.3.6,e^(n artanh(a x)) x^2 (c - a^2 c x^2)^p, which the parser folds intoT^(n/2).1/(a + b asinh(+-i + d x^2))^n. Rubi's six 7.1.5 rows, by the rule for the inverse hyperbolic sine of a quadratic, withg = cosh(u/2 + c pi/4):cosh(u/2) + c sinh(u/2)issqrt(2)times it, and its square is1 + c sinh(u) = c d x^2. They are complex at every x and are checked there.Chain against master f7f2a7a:
The ten still answer after the rebase onto 47ab958. The full unit suite passes locally: 16292 passed, 0 failed. The BREAKING-CHANGES lengths were re-measured on the branch, and two had moved.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura