The integral over the root of a square quadratic is its modulus's, not the table's

[Rafael-SOWNet]

Closes #1670.

The table's entry for k/sqrt(Q) and sqrt(Q) reads any quadratic Q = A x^2 + B x + C by the sign of A. When Q is a square that breaks: the arcsine divides by sqrt(B^2 - 4 A C), which is zero, and the logarithm is of 2 A (x + h) + 2 A |x + h|, which is zero on one side of the root. 1/((x - p) sqrt(Q)) writes Q in t = 1/(x - p), still a square, and asks the same entry.

The root of a square is the modulus of a linear, sqrt(A (x + h)^2) = sqrt(A) |x + h|, and the rule for a root of a perfect square already writes that. Now:

• The entry does not read a quadratic whose discriminant is zero, so the perfect-square rule gets it.
• The perfect-square rule takes a leading coefficient that is negative for a real parameter, -b^2 among them. sqrt(A s) = sqrt(A) sqrt(s) holds for any A when s is not negative, so the root of -(a + b x)^2 is sqrt(-b^2) |x + a/b|, and b^2 > 0 travels with the answer.
• The discriminant is evaluated with its symbols pinned first and simplified only where it is zero there, since the table asks this of every quadratic under a root it meets.

Compared at points on both sides of each root, a = 1.3, b = 0.7, c = 0.6, d = 1.9, h = 1.1:

integrand	master	this
1/sqrt(x^2 + 2 x + 1)	no value for x < -1	sgn(x + 1) ln(x + 1)
sqrt(x^2 + 2 x + 1)	no value for x <= -1	sgn(x + 1) (x^2/2 + x)
3/sqrt(9 x^2 - 6 x + 1)	no value for x < 1/3	right
1/sqrt(-4 - 4 x - x^2)	NaN	sgn(x + 2) ln(i x + 2 i)/i
sqrt(-4 - 4 x - x^2)	NaN	i sgn(x + 2) (x^2/2 + 2 x)
1/sqrt(-a^2 - 2 a b x - b^2 x^2)	NaN	right
x/sqrt(-a^2 - 2 a b x - b^2 x^2)	declined	right
1/(x sqrt(-a^2 - 2 a b x - b^2 x^2)), Rubi 1.2.1.2 #2737	NaN	right
1/(x sqrt(a^2 + 2 a b x + b^2 x^2))	no value between the roots	right
1/((d + h x) sqrt(a^2 + 2 a b x + b^2 x^2))	no value between the roots	right
1/((d + h x) sqrt(-a^2 - 2 a b x - b^2 x^2))	NaN	right
1/(x sqrt(c (a + b x)^2))	no value between the roots	declined

The last is declined because c has no known sign, so its square is not read as one.

Tests: RootOfAPerfectSquareIntegralTest.TheTableDoesNotReadASquareAsAQuadratic, eleven rows, and ASquareOfUnknownSignIsNotAnsweredWrongly, which takes a decline or an answer that holds everywhere. They compare at every point where the integrand has a value, so an answer with no value there fails instead of being skipped. All twelve fail on master.

Measured on the Rubi corpus against master 94ba5ff6, which has the same library as master now, with both builds side by side:

	master	this
family 0, independent suites (1814)	1758	1758
families 1 to 8, sampled (3967)	3480, 3 wrong	3482, 1 wrong
Rubi 1.2.3.2, the 179 whose trinomial is a square	107, 2 wrong, 8 past the budget	103, 0 wrong, 0 past the budget

Five problems moved in the sample, and I re-ran each alone on both builds:

• Rubi 1.2.1.1 Fix LaTeX for real intervals #97 sqrt(-4 + 12 x - 9 x^2) and LaTeXize infinity and tensors correctly #100 1/sqrt(-4 - 12 x - 9 x^2) were wrong on master and are right here.
• 1.2.1.2 The two documents that still deferred a scheduling policy say what was measured #1203 sqrt(c d^2 + 2 c d e x + c e^2 x^2)/(d + e x)^4 ran past the budget on master and is answered here in 2.6 seconds.
• 1.2.3.2 Additional definite integral testing #659 (a^2 + b^2/x^(2/5) + 2 a b/x^(1/5))^(5/2) ran past the budget on master and is declined here.
• 5.3.6 Add secant and cosecant #29 takes about 20 seconds on both builds, so its verdict under the 5-second budget depends on load. Alone, both builds answered it.

The four squares in 1.2.3.2 that master answers and this branch does not are #111, #574, #598 and #607. On master each has no value at 3 to 6 of 6 points when a b < 0, where the integrand has one. The corpus binds a and b to positive numbers, so it counted them as solved. The two wrong there, #645 and #647, are declined here too. 2.5.0 declines all six, so none of them changes against the release.

The suite passes, 14,324 tests on a fresh build, and so does the allocation gate.

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