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Why doesn't full_simplify() simplify?

I defined and integrated a gaussian:

from sage.symbolic.integration.integral import definite_integral
var('A,w,x')
assume(A, "real")
assume(w, "real")
assume(w > 0)
G(A,w,x)=A*(2*sqrt(ln(2)/pi)/w) * exp(-4*ln(2)*(x/w)^2)
a=definite_integral(G(A,w,x),x,-infinity,infinity)
a.full_simplify()
> sqrt(pi)*A*sqrt(log(2)/pi)/sqrt(log(2))

It's trivial to see that the answer is just A; why doesn't simplify simplify?