AngouriMath
SolveByPartsAgainstALogarithmOfARadicalSum(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
A power of x times the logarithm of A + B sqrt(Q) , for polynomials A ,
B and Q , by parts, with the logarithm's derivative written over the conjugate:
withD = A^2 - B^2 Q , it is
D'/(2 D) + (Q (A B' - A' B) + A B Q'/2)/(D sqrt(Q)) , a rational function and one over
the root, which the rules for those answer. Rubi's 3.5,
x^3 ln(-1 + 4 x + 4 sqrt((x - 1) x)) , where D = 8 x + 1 .
https://github.com/asc-community/AngouriMath/issues/233
with
the root, which the rules for those answer. Rubi's 3.5,
https://github.com/asc-community/AngouriMath/issues/233
Remarks
The search differentiates the logarithm as written, a quotient with the root in both
parts, and ran past the budget on what was left. Only for aD that is not a
constant: for one that is,ln(x + sqrt(x^2 + 1)) and the other inverse hyperbolic
functions, the derivative is the root's alone, and the rules for those answer them.
The derivative is an identity of the algebra,sqrt(Q)^2 = Q , with no branch in it.
parts, and ran past the budget on what was left. Only for a
constant: for one that is,
functions, the derivative is the root's alone, and the rules for those answer them.
The derivative is an identity of the algebra,
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