AngouriMath
SolveAPolynomialTimesARationalFunctionOfAnExponential(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A polynomial in x times a rational function of exponentials of x ,
by parts against the whole rational function:x tanh(x)^2 is
x ((e^(2x) - 1)/(e^(2x) + 1))^2 , whose antiderivative under u = e^(2x) is
x - tanh(x) , a polynomial and a rational function of the exponential again,
and what parts leaves isx - tanh(x) itself, a degree lower in x .
by parts against the whole rational function:
and what parts leaves is
Remarks
each term on its own, and each term's antiderivative in
of
leaves
search that found nothing. Here the rational function goes to the exponential
substitution whole, and where its antiderivative keeps a logarithm of an
exponential's sum the integrand is declined at once:
elementary, and this says so in a millisecond.
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