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Symbolics for .NET


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

 Method (no overloads)

Summary

x^p for a power that does not hold the variable: the power
rule, or the logarithm where the power rule would divide by zero.

Remarks

The exponent is normalised before it is read.x^(-3 + 1 + 1) is
x^(-1), but the sum is not the integer, so comparing the written form against
-1 missed the logarithmic case and applied the power rule to it — producing
x^(-3 + 1 + 1 + 1)/(-3 + 1 + 1 + 1), which is x^0/0, which is
NaN. That is a claim that no antiderivative exists where one plainly does, and
it reached the caller: (a^2 + 2abx^2 + b^2x^4)^3/x^7 came back NaN + C while the same integrand written (a + bx^2)^6/x^7 was answered.
https://github.com/asc-community/AngouriMath/issues/1258
And normalised again on the way out, which is the other half and the half that
explains where such an exponent comes from. This rule used to return p + 1 standing as a sum, so an answer handed back in as an integrand — which is exactly what
repeated integration by parts does — accumulated one + 1 per round until a
round landed on -1 spelled as a sum. The rule was feeding itself the one input
it could not read.
 A symbolic exponent is left to the power rule as before. int x^n dx is
x^(n+1)/(n+1) for every n but -1, and this does not decide
whether an undecidable n is that one; what it fixes is an exponent that
is decidable and was read as though it were not.
 Decidable includes a symbol that cancels: x^(-1 - 3n + 3n) is x^(-1) for
every n, and is what expanding x^(-1 - 3n) (a + b x^n)^3 leaves for its
last term, but InnerSimplified keeps -3n + 3n as two terms,
so the exponent plus one is asked whether it vanishes as a value. Read as written it
was x^0/0 again, and the whole answer had no value anywhere; Rubi's 1.1.3.2
has four such and 1/(a (b x^m)^n)^(1/(m n)), which is x^(-m n/(m n)).

























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