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I am wondering if the function below is Integrable:

$$\frac{\exp{(-\frac{1}{2}(u-2)^2-2u^2)}}{u-2}$$

When I work it out on computer, the integral is finite from -Inf to Inf. But clearly it has a pole at u=2. Is this pole integrable? If yes, what kind of coordinate transform is required?

Any help is appreciated!

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# I Non-Integrable Function

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