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Hi Ben
For special values of the constants there are no differences in the integral and the plot:
A=integrate(100exp(-1/2x^2/8^2)*cos(x),x,algorithm='mathematica_free');
L=[[l,numerical_integral(100exp(-1/2x^2/8^2)*cos(x),0,l)[0]] for l in srange(-6,6,0.1)];
list_plot(L,plotjoined=True)
