AngouriMath
OverThePowerOfTheMonicQuadraticInNamedCoefficients(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,System.Int32,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
∫ N(x)/(a x^2 + b x + c)^n dx as 1/a^n times the integral over
(x^2 + k x + m)^n , with k = b/a and m = c/a each a fresh symbol
while it is integrated, where IntegrateRationalOverPowerOfQuadratic(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,System.Int32,AngouriMath.Entity.Variable,System.Boolean) declined the quadratic as written.
while it is integrated, where IntegrateRationalOverPowerOfQuadratic(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,System.Int32,AngouriMath.Entity.Variable,System.Boolean) declined the quadratic as written.
Remarks
With symbols in both a and c the divisions by the quadratic leave
remainders the reduction cannot read as linear:x^5/(a + b x + c x^2)^4 was
declined, wherex^5/(k + m x + x^2)^4 and x^5/(2 + b x + c x^2)^4 are
answered in a few hundred milliseconds. Rubi's 1.2.1.2. A leading coefficient that is a
number as written, such as the1 * 1^2 a substitution leaves, is not one: the
substitution that wrote(b d + 2 c d x)^8/(a + b x + c x^2)^3 in the quadratic
asks with one, and naming its other two took the answer from 65,236 characters to 202,057.
https://github.com/asc-community/AngouriMath/issues/718
remainders the reduction cannot read as linear:
declined, where
answered in a few hundred milliseconds. Rubi's 1.2.1.2. A leading coefficient that is a
number as written, such as the
substitution that wrote
asks with one, and naming its other two took the answer from 65,236 characters to 202,057.
https://github.com/asc-community/AngouriMath/issues/718
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