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## Homework Statement

Test the following integral for convergence:

[tex] \int^{∞}_{-∞}\frac{dx}{\sqrt{x^{4}+1}} [/tex]

## Homework Equations

## The Attempt at a Solution

I was able to use the ratio test to show that the integral converges if and only if [itex] \int^{∞}_{-∞}\frac{dx}{x^{2}} [/itex] converges, but I haven't been able to show whether this particular integral converges or diverges.

This integral is not continuous, but it is almost continuous since the discontinuity is a countable set.

NOTE: The integral on the bottom actually diverges, and yet the original integral converges!!! But HOW?!!!

BiP

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