AngouriMath

Symbolics for .NET


Table of contents

AngouriMath

Navigation
Home Quick start Wiki Almanac Research What's new Try Use Angouri.org GitHub Report a bug Donate Contacts

← Back to list of members

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

 Method (no overloads)

Summary

K L^m/Q^n for a quadratic Q = A x^2 + B x + C, a linear L a multiple
lambda of its derivative and an odd m >= 3, in u = Q: L^m dx is
lambda^m (Q')^(m - 1) du, and (Q')^2 = 4A u + B^2 - 4AC, so the integrand is
K lambda^m (4A u + B^2 - 4AC)^((m - 1)/2)/u^n, a polynomial over a power of u.
null for anything else.

Remarks

Rubi's 1.2.1.2 has (b d + 2c d x)^9/(a + b x + c x^2)^3; through the partial fractions
its answer was seventy-six thousand characters, with a case for each sign of the
discriminant, where in u it is a sum of a few powers.
https://github.com/asc-community/AngouriMath/issues/718

























Angouri © 2019-2023 · Project's repo · Site's repo · Octicons · Transparency · 4862 pages online