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

 Method (no overloads)

Summary

A product of roots that is a constant times a whole power of the variable, though
written with it, beside something else: with A the roots and r the sum of
their exponents times the degrees of what is under them, K = A/x^r has the
derivative zero wherever it is real, and integral A T dx = K integral x^r T dx.
sqrt(b - a/x^2)/sqrt(a - b x^2) is K/x, with K^2 = -1.

Remarks

r is the degree of A both at infinity and at zero, which a constant times
x^r needs, and K is taken as constant only where its derivative is zero at
the sampled points; the answer is checked. Rubi's 4.7.7
sin(x) sqrt(b - a/x^2)/sqrt(a - b x^2), which is K Si(x), was declined.
Late, where everything reading the integrand as written has declined.
https://github.com/asc-community/AngouriMath/issues/233

























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