\int _{ -\infty }^{ \infty }{ \frac { { e }^{ -y } }{ { y }^{ 2 }+1 } } converges \quad or\quad diverge?

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\int _{ -\infty }^{ \infty }{ \frac { { e }^{ -y } }{ { y }^{ 2 }+1 } } converges \quad or\quad diverge?

OCW Scholar - Single Variable Calculus
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\int\limits _{ -\infty }^{ \infty }{ \frac { { e }^{ -y } }{ { y }^{ 2 }+1 } } converges \quad or\quad diverege? \]
Diverges because from minus infinity to zero the expression e^-y is much much larger than y^2+1. Actually because you take the integral from minus infinity to infinity this holds:\[\int\limits_{-\infty}^{\infty}\frac{ e^-y }{ y^2+1 }dy = \int\limits_{-\infty}^{\infty}\frac{ e^y }{ y^2+1 }dy \]
diverges. take simple example of \[\int\limits_{-infinity}^{infinity}(e^x)dx is \not convergent. and whether you divide \it by X^2 +1 .\] that is a positive no....wont effect as we are talkin about infinity/infinty

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