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Consider integrating the following rational function
> f := (6*x^5+6*x^2-4*x+8*x^3-4)/(x^6+2*x^3-2*x^2+1);
The difficulty in this example is that the denominator does not factor
over Q,
hence we cannot use the traditional method of splitting the rational
function into partial fractions.
The Trager-Rothstein algorithm implemented in Maple V yields
the nice result
That is, there are two logs corresponding to two roots 
of the
polynomial 
. Hence, Maple obtains
> int(f,x);
An improvement to this algorithm due to Rioboo is implemented in Release 2.
It seeks to obtain a real result from a real integrand with no new poles.
For example (note: in Maple V this integral returned complex logs),
> f := (x^4-3*x^2+6)/(x^6-5*x^4+5*x^2+4);
> int(f,x);
