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SolveALogarithmicDerivativeOfARadicalSum(AngouriMath.Entity,AngouriMath.Entity.Variable)

Method (no overloads)

Summary

An integrand that is a constant multiple of D'/D for a sum D below the
bar holding a root, decided at sampled points and answered as that multiple of
ln(D).

Remarks

Hearn's x((x^2 - 1) sqrt(x^2 - 4) + (x^2 - 4) sqrt(x^2 - 1))/((x^2 - 1)(x^2 - 4)(1 + sqrt(x^2 - 4) + sqrt(x^2 - 1))) is (x/sqrt(x^2 - 4) + x/sqrt(x^2 - 1))/(1 + sqrt(x^2 - 4) + sqrt(x^2 - 1)), the
derivative of its denominator over it, and the substitution that reads
u = D was declined for the quotient by D' it could not simplify --
(x^2 - 1) sqrt(x^2 - 4)/((x^2 - 1)(x^2 - 4)) is 1/sqrt(x^2 - 4) only
with the root's square read as the radicand -- and the search around it ran past
the budget. The quotient f D/D' is evaluated at points instead: where it is
the same rational number at each, f is that number times D'/D, and the
answer is checked against the integrand at sampled points before it is returned,
as the ansätze check theirs.
https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

Table of contents

AngouriMath

SolveALogarithmicDerivativeOfARadicalSum​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

SolveALogarithmicDerivativeOfARadicalSum(AngouriMath.Entity,AngouriMath.Entity.Variable)