Integrate a constant over x squared times the root of a quadratic (#233)

[Rafael-SOWNet]

"1 / (x ^ 2 * sqrt(x ^ 2 - 1))".Integrate("x")
// master: integral(1 / (x ^ 2 * sqrt(x ^ 2 - 1)), x)

The shape a trigonometric substitution is usually taught for, and one of the ones named in #233's list of what is missing.

No substitution needed to state the answer

Differentiating sqrt(ax² + c)/x gives -c/(x² · sqrt(ax² + c)) exactly. So the whole family is one formula, and there is no case analysis over the signs of a and c to get wrong:

1/(x²√(x²−1))	root of a difference
1/(x²√(x²+1))	root of a sum
1/(x²√(1−x²))	sign of x² the other way
1/(x²√(4−x²)), 1/(x²√(2x²+3))	with coefficients
3/(x²√(x²−4)), 1/(2x²√(x²+9)), −1/(x²√(x²+1))	a constant anywhere in the quotient

What it refuses

A radicand with a linear term, or with either coefficient zero. A zero constant term is what the formula divides by; with a zero a there is no root of x left to speak of. Both are left unevaluated and pinned as such.

Verification

17 tests, 8 of which fail without the change, each checked by differentiating the answer back and comparing at points. 4026 unit tests and 127 F# tests on both target frameworks, none failing. 117-problem self-verifying corpus at 102/117 — int:trig-sub goes from 67% to 100% — with nothing wrong, in error or timing out.

[codecov-commenter]

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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 80.46%. Comparing base (90c00a8) to head (5a1459e).
⚠️ Report is 58 commits behind head on master.
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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #691      +/-   ##
==========================================
- Coverage   80.99%   80.46%   -0.54%     
==========================================
  Files         155      156       +1     
  Lines       13687    12953     -734     
  Branches     1957     2130     +173     
==========================================
- Hits        11086    10422     -664     
+ Misses       1990     1922      -68     
+ Partials      611      609       -2     

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