sympy seems to be able to handle some integrals that maxima doesn't:
{{{
sage: f=1/(x^4+x^3+1)
sage: fm=f._maxima_()
sage: fm.integrate()
'integrate(1/(x^4+x^3+1),x)
sage: fs=f._sympy_()
sage: fs.integrate()
RootSum(229*_t**4 + 6*_t**2 + _t + 1, Lambda(_t, _t*log(-37785*_t**3/3547 -
5496*_t**2/3547 + 12979*_t/3547 + x + 691/3547)))
}}}
The problem is that sage hasn't the appropiate symbolic object to handle
RootSum (which is the sum of a expression over the roots of a polynomial).
Should we introduce these kind of symbolic objects? This is the standard
way to compute integrals of rational functions (IIRC, that is what the
Risch algorithm does, for example). Wolfram Alpha returns a different
expression, but still a sum over the roots of a polynomial.
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