AngouriMath
AsTheDerivativeOfALowerPowerOfALinearBesideAFunction(System.Collections.Generic.IReadOnlyList{AngouriMath.Entity},AngouriMath.Entity.Variable)
Method (no overloads)
Summary
A sum whose terms are not elementary apart, integrated by parts the other way in some of the terms that are a
powerL^(-k) , k >= 2 , of one linear L beside a function F with x only inside transcendental functions -- the power integrated, Q = L^(1 - k)/((1 - k) L') , and F differentiated -- where what that leaves, -Q F' , cancels against the other terms: then the sum is
(Q F)' summed over those terms. psi_1(a + b x)/x^2 - b psi_2(a + b x)/x is
(-psi_1(a + b x)/x)' , Rubi's 8.6, and neither of its terms is elementary.
https://github.com/asc-community/AngouriMath/issues/2075
power
https://github.com/asc-community/AngouriMath/issues/2075
Remarks
Some, not all: in psi_1(x)/(2 + 3 x)^3 - psi_2(x)/(6 (2 + 3 x)^2) the second term has a power of -2 as well,
and is what the first leaves. So each set of them is tried, the smallest first, and rejected at a point by adding
numbers before anything is simplified. Nothing is asked, so a remainder that does not cancel declines rather than
becoming a question: lowering the power towardL^(-1) raises the order of F , and a remainder in
F' is no nearer an answer.
and is what the first leaves. So each set of them is tried, the smallest first, and rejected at a point by adding
numbers before anything is simplified. Nothing is asked, so a remainder that does not cancel declines rather than
becoming a question: lowering the power toward
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