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## Main Question or Discussion Point

I am interested in the integral

[tex]\int e^{2 \pi i \left( x^3+ax^2+bx \right) } dx[/tex]

Since [tex]\int e^{-x^2} dx[/tex] 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 go about solving it?

If it is not integrable, does anyone have any idea how to most efficiently evaluate it numerically (from say 0 to an arbitrary [tex]x_0[/tex])?

[tex]\int e^{2 \pi i \left( x^3+ax^2+bx \right) } dx[/tex]

Since [tex]\int e^{-x^2} dx[/tex] 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 go about solving it?

If it is not integrable, does anyone have any idea how to most efficiently evaluate it numerically (from say 0 to an arbitrary [tex]x_0[/tex])?