Option variable
integrate_use_rootsof
Default value: false
When integrate_use_rootsof
is true
and the denominator of
a rational function cannot be factored, integrate
returns the integral
in a form which is a sum over the roots (not yet known) of the denominator.
For example, with integrate_use_rootsof
set to false
,
integrate
returns an unsolved integral of a rational function in noun form:
(%i1) integrate_use_rootsof: false$ (%i2) integrate (1/(1+x+x^5), x); / 2 [ x - 4 x + 5 I ------------ dx 2 x + 1 ] 3 2 2 5 atan(-------) / x - x + 1 log(x + x + 1) sqrt(3) (%o2) ----------------- - --------------- + --------------- 7 14 7 sqrt(3)
Now we set the flag to be true and the unsolved part of the integral will be expressed as a summation over the roots of the denominator of the rational function:
(%i3) integrate_use_rootsof: true$ (%i4) integrate (1/(1+x+x^5), x); ==== 2 \ (%r4 - 4 %r4 + 5) log(x - %r4) > ------------------------------- / 2 ==== 3 %r4 - 2 %r4 3 2 %r4 in rootsof(x - x + 1) (%o4) ---------------------------------------------------------- 7 2 x + 1 2 5 atan(-------) log(x + x + 1) sqrt(3) - --------------- + --------------- 14 7 sqrt(3)
Alternatively the user may compute the roots of the denominator separately,
and then express the integrand in terms of these roots,
e.g., 1/((x - a)*(x - b)*(x - c))
or 1/((x^2 - (a+b)*x + a*b)*(x - c))
if the denominator is a cubic polynomial.
Sometimes this will help Maxima obtain a more useful result.