Comment #32 on issue 2010 by [email protected]: Integration with the full Risch Algorithm
http://code.google.com/p/sympy/issues/detail?id=2010
OK, I see now that even integrate() can't do your integral integrate(sy.exp(2*alpha1**2*x**2 + (4*alpha1*alpha2 - 2)*x + 2*alpha2**2), x). risch_integrate() won't have a hope of computing this until the day that erf() extensions are added to the code, which won't be for a while unless someone else jumps on doing it (I personally have unfortunately not been very active with it, and my personal priorities are in other parts of the integrator anyway).
To give the other integrators a better chance, I would recommend completing the square in the exponential, so that you have something of the form exp(a*(x - b)**2 + c), which you should write as exp(a*(x - b)**2)*exp(c). Really, one of the integrators (probably meijerg) should do this for you. Can you open a new issue for this?
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