AngouriMath
SolveAPowerOfALinearBesideTheDerivativeOfAQuadraticOverItsPower(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A power of a linear beside the derivative of a quadratic, over a whole power of that
quadratic, by parts once:Q' L^m/Q^n with u = L^m and
dv = Q'/Q^n dx is -L^m/((n - 1) Q^(n - 1)) + m e/(n - 1) * integral L^(m - 1)/Q^(n - 1) ,
forL = d + e x , and the power of the quadratic is one lower in what is left.
quadratic, by parts once:
for
Remarks
Rubi's 1.2.1.3 (b + 2 c x) sqrt(d + e x)/(a + b x + c x^2)^2 and its kin took
thirty seconds or ran past the budget, the partial fractions taking the symbolic
quadratic apart twice over; what is left over its first power is answered in a third of
a second -- a whole power of the linear too, `(b + 2 c x) (d + e x)^4/(a + b x + c x^2)^2`
ran past the budget there. The numerator is read up to a constant multiple ofQ' .
https://github.com/asc-community/AngouriMath/issues/718
thirty seconds or ran past the budget, the partial fractions taking the symbolic
quadratic apart twice over; what is left over its first power is answered in a third of
a second -- a whole power of the linear too, `(b + 2 c x) (d + e x)^4/(a + b x + c x^2)^2`
ran past the budget there. The numerator is read up to a constant multiple of
https://github.com/asc-community/AngouriMath/issues/718
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