AngouriMath
SolveByTheDerivativeOfAQuadraticAsTheVariable(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A power of a linear that is a constant multiple of a quadratic's derivative, beside a
power of the quadratic, under the linear as the variable: witht = λ (b + 2 c x) the quadratic a + b x + c x^2 is (t^2/λ^2 - Δ)/(4 c) , with
Δ = b^2 - 4 a c , so t^m Q^p is a binomial in t . Rubi's 1.2.1.2,
(b d + 2 c d x)^m (a + b x + c x^2)^p , which it substitutes the same way.
power of the quadratic, under the linear as the variable: with
Remarks
The substitution is affine, so the integrand in t is the integrand exactly. The
quadratic is written int from its coefficients rather than by substituting:
substituted, it keeps a linear term that is zero as a value and not as written, and the
rules for a binomial readα + β t^2 . Only where a power is not whole: a rational
function is the partial fractions'.
https://github.com/asc-community/AngouriMath/issues/718
quadratic is written in
substituted, it keeps a linear term that is zero as a value and not as written, and the
rules for a binomial read
function is the partial fractions'.
https://github.com/asc-community/AngouriMath/issues/718
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