AngouriMath
SolveAnExponentialInTheReciprocalOfALinearOverAnotherLinear(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
An exponential of a constant plus a multiple of the reciprocal of a linear over a whole
power of another linear,F^(a + b/(c + d x))/(g + h x)^n , under
SolveAnExponentialInTheReciprocalOfALinear(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)'s substitutionu = 1/(c + d x) ,
asked before the rules that do not read it: inu it is
-d^(n - 1) u^(n - 2) F^(a + b u)/((d g - c h) u + h)^n , the exponential integral of a
shifted argument, which SolveAnExponentialOfALinearOverAPowerOfALinear(AngouriMath.Entity,AngouriMath.Entity.Variable) and
SolveAnExponentialOverSeveralLinears(AngouriMath.Entity,AngouriMath.Entity.Variable) answer. The exponent may be written
e + f (a + b x)/(c + d x) . Rubi's 2.3.
https://github.com/asc-community/AngouriMath/issues/233
power of another linear,
SolveAnExponentialInTheReciprocalOfALinear(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)'s substitution
asked before the rules that do not read it: in
shifted argument, which SolveAnExponentialOfALinearOverAPowerOfALinear(AngouriMath.Entity,AngouriMath.Entity.Variable) and
SolveAnExponentialOverSeveralLinears(AngouriMath.Entity,AngouriMath.Entity.Variable) answer. The exponent may be written
https://github.com/asc-community/AngouriMath/issues/233
Remarks
In its place at the end of the dispatch the substitution was reached only after every rule
above it had declined, andF^(e + f (a + b x)/(c + d x))/(g + h x)^n took 2 to 10
seconds and 0.4 to 12 GB forn = 1 to 4, past the budget for 3 and 4, for the answer
it writes in a twentieth of a second. Only for an exponent linear inu and another
linear below the bar whose slope inu , d g - c h , is not zero as a value. A
multiple ofc + d x is not another linear, though a power of c + d x alone
arrives as one, written monic: its elementary cases are the ansatz's, which writes them
shorter, and SolveAnElementaryMomentOfAnExponentialInAPowerOfTheReciprocal(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)'s.
Another linear above the bar only, and a Gaussian inu , keep the rule's place.
above it had declined, and
seconds and 0.4 to 12 GB for
it writes in a twentieth of a second. Only for an exponent linear in
linear below the bar whose slope in
multiple of
arrives as one, written monic: its elementary cases are the ansatz's, which writes them
shorter, and SolveAnElementaryMomentOfAnExponentialInAPowerOfTheReciprocal(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)'s.
Another linear above the bar only, and a Gaussian in
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