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AngouriMath

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SolveByAPowerOfXWithASymbolicExponent​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean)

 Method (no overloads)

Summary

A function of x^n for a symbolic n beside a power of x,
x^m R(x^n) with (m + 1)/n rational, under u = x^(n/d): Rubi's
x^(-1 + 4n)/(a + b x^n + c x^(2n)) and x^(-1 + n/4)/(b x^n + c x^(2n)).

Remarks

With g = x f(x), int f dx = (d/n) int g/u du, since dx/x = (d/n) du/u;
and every power x^t in g is u^(t d/n), a whole power of u where t d/n is a whole number, which makes it the same value for every
x. The search reads x^(2n) as a power of x^n only for a number
n, and found no candidate for x^(n/4), which is not written; so these
were declined. The powers of x are gathered first, x x^(-1 + 4n) into
x^(4n), and the unit is each exponent left, divided by up to six.
https://github.com/asc-community/AngouriMath/issues/718
 A factor (c x)^t is read as x^t, with (c x)^t x^(-t) in front of the
answer: its derivative is zero wherever it is defined, so it is a constant on each
interval of the domain, for either sign of c. Read as it was written, Rubi's
(c x)^(-1 - 2n/3)/(a + b x^n) left an x outside every power of x and was declined.
https://github.com/asc-community/AngouriMath/issues/233

























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