[Rafael-SOWNet]

x^4 (a + b atanh(c x)) (d + e ln(1 - c^2 x^2)), the other powers of x up to x^5, and their arcoth twins were declined. Write y = c x, T for the inverse function and B = ln(1 - y^2). The derivatives T' = 1/(1 - y^2) and B' = -2 y/(1 - y^2) are rational. The integral of y^j T B is p0 T B + p1 T + p2 B + q1 T^2 + q2 B^2 + r, for polynomials p0, p1, p2 and r and constants q1 and q2. The constants are chosen so that each division by 1 - y^2 is exact.

Only the two derivatives are read, so the answer holds for the artanh and the arcoth alike, and for any constant factor inside the logarithm. The rule applies only where the product T B is in the integrand. Where c is a number, it leaves the integrand to the rules after it, which already answer the even powers of x, so atanh(2 x) ln(1 - 4 x^2) keeps its answer.

Measured on 8a1ef454, branch against master:

Run	Problems	Master	Branch
Pocket: Rubi's 7.3.4 and 7.4.1	352	338 solved	347 solved
Family 1, 40 a file	1,381	1,362	1,362
Family 0, whole	1,814	1,789	1,789
Families 2 to 8, sampled	2,410	2,362	2,362

Re-run alone on both builds, 10 problems go from timed out to answered, in 29–274 ms: Rubi's 7.3.4:649–653 and 7.4.1:361–363, 367 and 368.

Two problems master answers in 23–24 s, 3.2.1:292 and 3.5:37, timed out on the branch when re-run alone. At a 60 s budget both builds answer them, and the allocations agree to within 0.01% (34.2 GB and 37.0 GB), so the branch does not reach them. 7.4.1:161 is answered on both in 21 s. None of the problems answered on both builds allocates more on the branch. No run had a wrong answer.

APolynomialTimesAnInverseHyperbolicTangentAndTheLogarithmOfItsQuadraticIntegralTest differentiates the answers back. BREAKING-CHANGES.md has the entry, with the 2.5.0 column measured on v2.5.0.

Part of #233.

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