Check out the most popular debate in improper integrals: The integral of 1/x from -1 to 1, is it divergent or equal to 0 https://youtu.be/dHwrzLDmdT8

integral of 2/(x^2-1) from 1 to inf (both type 1 and type 2),
type 1 improper integral: the length of the interval of the integration is infinite



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