Comment #4 on issue 2040 by smichr: Better way to make a rational function out of an expression
http://code.google.com/p/sympy/issues/detail?id=2040

Hopefully that will work in polys11 with the new changes that Matteusz has made since in sympy live I get the following when trying to factor the interior of the original sqrt you posted:

log(x**2 + 3*x + 2)*(log(x + 1) + log(x + 2))
(log(1 + x) + log(2 + x))*log(2 + 3*x + x**2)
factor(_)
Traceback (most recent call last):
File "/base/data/home/apps/sympy-live/1.338726892805923919/shell.py", line 351, in get
    exec compiled in statement_module.__dict__
  File "<string>", line 1, in <module>
File "/base/data/home/apps/sympy-live/1.338726892805923919/sympy/polys/factortools.py", line 80, in factor
    coeff, factors = poly_factors(f, *symbols, **flags)
File "/base/data/home/apps/sympy-live/1.338726892805923919/sympy/polys/factortools.py", line 20, in poly_factors
    f = Poly(f, *symbols)
File "/base/data/home/apps/sympy-live/1.338726892805923919/sympy/polys/polynomial.py", line 454, in __new__
    terms = Poly._decompose(poly, *symbols)
File "/base/data/home/apps/sympy-live/1.338726892805923919/sympy/polys/polynomial.py", line 598, in _decompose
    raise PolynomialError("Can't decompose %s" % factor)
PolynomialError: Can't decompose log(1 + x)

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