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You do what we call an "improper integral".

I will denote the integral of f from a to b as intl a-b (f) here.

so we define intl a-infinity (f) as lim b->infinity a-b(f)

So it is a limit, and just like all other integrals, it may or may not exist (+/- infinity or infinite uncountable oscilations etc.)

You have have to prove yourself though about its properties (it's easy since I reduced it to the regular integral) and you will see it's a perfectly fine definition.

If you want examples, I have lots, message me.

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Q: How do you calculate integrals that go to infinite?
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