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    Is this non-integrable?

    I am interested in the integral \int e^{2 \pi i \left( x^3+ax^2+bx \right) } dx Since \int e^{-x^2} dx is non-integrable, I suspect this integral may be too, but I am not so sure because of the exponent being imaginary. Does anyone know? If it is integrable, does anyone have any idea how to...