AngouriMath
SolveAnElementaryMomentOfAnExponentialInAPowerOfTheReciprocal(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
An exponential of a constant plus a multiple of a power of the reciprocal of a linear,
over a power of the linear, where the integral is elementary:
F^(a + b/(c + d x)^k)/(c + d x)^n with k >= 2 and n - 1 a positive
multiple ofk . Under SolveAnExponentialInTheReciprocalOfALinear(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)'s
u = 1/(c + d x) it is -(1/d) u^(n - 2) F^(a + b u^k) , and under w = u^k a
polynomial inw times F^(a + b w) , which the question in u is answered by.
Rubi's 2.3. https://github.com/asc-community/AngouriMath/issues/233
over a power of the linear, where the integral is elementary:
multiple of
polynomial in
Rubi's 2.3. https://github.com/asc-community/AngouriMath/issues/233
Remarks
In the substitution's place at the end of the dispatch these were reached after every rule
above it had declined:F^(a + b/(c + d x)^2)/(c + d x)^13 took 6 seconds and 6 GB,
F^(a + b/(c + d x)^3)/(c + d x)^13 and higher ran past the budget, and the questions
inu take a hundredth of a second. The power below the bar arrives written monic,
c/d + x beside the c + d x of the exponent, and is read as a constant multiple
of the linear by value. Only where the integral is elementary, and only for a linear other
than the variable: asked here for every power, the exponential integral and the error
function came out longer or slower than where they are answered now, a linear exponent in
u , which the ansatz answers in the base, three times longer, and the moments of
f^(a + b/x^2) , answered in a hundredth of a second already, respelled.
above it had declined:
in
of the linear by value. Only where the integral is elementary, and only for a linear other
than the variable: asked here for every power, the exponential integral and the error
function came out longer or slower than where they are answered now, a linear exponent in
Angouri © 2019-2023 · Project's repo · Site's repo · Octicons · Transparency · 4862 pages online