AngouriMath
SolveALogarithmOrAnArctangentOfAPolynomial(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
The logarithm, arctangent or arccotangent of a polynomial in x ,
by parts against one, closed:x f(P) - int x f'(P) P' , whose remainder is a
rational function --x P'/P , x P'/(1 + P^2) -- and goes to the rational
integrator directly.
by parts against one, closed:
rational function --
integrator directly.
Remarks
By parts against one is a rule of the top: a nested step's remainder answered that
way let a doomed search above it carry on. Soln(1 + x^2) one level down had no
antiderivative, and every remainder that held it -- what parts leaves from
arctan(x) ln(1 + x^2) with the arctangent differentiated, for one -- was
declined for want of it. This is the same step for the one shape whose remainder is
closed, and it is closed itself, so it is answered at any depth.
way let a doomed search above it carry on. So
antiderivative, and every remainder that held it -- what parts leaves from
declined for want of it. This is the same step for the one shape whose remainder is
closed, and it is closed itself, so it is answered at any depth.
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