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SolveByDividingByAnExponential(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)

Method (no overloads)

Summary

A quotient by an exponential, handed on as the product with its reciprocal:
N/b^(f(x)) as N * b^(-f(x)).

Remarks

sin(x) * e^(-x) had an antiderivative and sin(x)/e^x did not. They are
the same integrand, and the difference is only which node is on top: integration by
parts matches a Mulf and nothing else, so a quotient never reached it. The
simplifier does not turn one into the other — it keeps sin(x)/e^x as written —
so nothing upstream closed the gap either.
The family is wider than the trigonometric case that exposed it: x/e^x,
ln(x)/e^x and sin(x)/2^x were all declined for the same reason, and each
is answered once written as a product.
Only an exponential denominator — a base free of the variable with the variable
in the exponent. x^n in a denominator is a rational function and belongs to
partial fractions, which reads it as written; turning that into a negative power would
take it away from the rules that answer it. A numerator free of the variable is left
alone too, since SolveAsPolynomialTerm(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) already takes that one.
https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

Table of contents

AngouriMath

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

SolveByDividingByAnExponential(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)