(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the Gaussian integral:

[itex]I = \int_{-\infty}^{\infty} e^{-x^2-4x-1}dx [/itex]

(That's all the information the task gives me, minus the [itex]I=[/itex], I just put it there to more easily show what I have tried to do)

2. The attempt at a solution

I tried to square [itex]I[/itex] and get a double integral:

[itex]I^2 = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} e^{(-x^2-4x-1)+(-y^2-4y-1)}dxdy [/itex]

and then my plan was to convert to polar-coordinates, however, this is my first time ever with double-integrals and/or switching to polarcoordinates, and I am kind of lost because every single example on the internet use the standard [itex]e^{-x^2}[/itex] gaussian function(and it is easy to see [itex]r^2=x^2+y^2[/itex]). Anyone who can push me in the right direction(I'm not even sure what finding the Gassuian integral means(?))?

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# Finding a Gaussian integral

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