A polynomial or a power of x beside exponentials of quadratics without a linear part is integrated about 0

[Rafael-SOWNet]

Part of #1501. Follows #1521.

#1521 integrated a product of exponentials of quadratics beside a polynomial by taking each term's moments at its square's centre, u = x + b/(2a). Where a term's exponent has no linear part, that shift is 0/(2a). Simplified, that is 0 provided not a = 0, and substituted into the polynomial it is not read as zero, so the polynomial was not read as one. x^2 sinh(a + b x^2)^3 was declined that way, as #1521 said.

Such a term's moments are now taken about 0, from each power of x and its coefficient. A power of x is read apart from the polynomial, above or below the bar. Below it, it is a negative power, and a negative even power is a moment too: sinh(a + b x^2)^3/x^2 is answered. A negative odd power ends at the exponential integral, and is still declined.

A term with a linear part keeps the polynomial as the integrand writes it, and its moments at the centre are taken as #1521 took them.

The two comments in #1521 that recounted how its first version failed now say only why the code is written as it is.

integral	master	this PR
x^2 sinh(a + b x^2)^3, sinh(a + b x^2)^3/x^2 (Rubi's 6.1.3)	unevaluated	answered
cosh(a + b x^2)^3/x^4	answered, after 52 s	answered, in 0.2 s
sinh(a + b x^2)^3/x	unevaluated	unevaluated: it ends at the exponential integral

Measured

Measured with the change on #1521's head before its merge (95361819), before the rebase onto #1520 and #1522. After the rebase, the library builds for every target, and the exponentials-of-quadratics, Gaussian and logarithm test classes pass (94).

• Rubi's problems whose answer uses erf, erfc or erfi: 811 across families 0 to 7, at a 3 s budget. This PR solves 722, where Exponentials of quadratics beside sines, cosines and hyperbolic functions of quadratics are integrated onto the Gaussian #1521 solves 720, with 0 wrong and nothing lost. Both have the same 3 timeouts, and the total time goes from 298 s to 264 s. The 2 gained are the two in 6.1.3 above.
• The textbook suites (family 0) are unchanged: 1723/1778, 0 wrong, 0 timeouts.
• The unit suite passes on net10.0: 12970 passed, 14 skipped, none failed, of 12984. One of the new test's rows was then cosh(a + b x^2)^2/x^4, which another rule answers, in 10 s: the rule here declines it, since the constant term of cosh^2 beside x^(-4) is left to the power rule. That row is now cosh(a + b x^2)^3/x^4, whose terms are all moments about 0, and the class passes in under a second.
• The allocation gate passes on all 19 gated benchmarks, with no allocation moved.

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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura