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FindFit with a sophisticated function (integral)

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simpler functions (two polynomials), that is the model. ...
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1answer
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Solving one equation, then inputting the values into another for NonlinearModelFit

Considering the equation a*x^3 + a*x^2 + x + b == 0 I'm looking to find the best value for a and ...