How can I solve:
$\int^\infty_{-\infty} \frac{1}{y^2+1} dy$
I have tried splitting it up in two limits:
$\lim\limits_{n \to \infty} [arctan(y)]^n_0 + \lim\limits_{n \to \infty} [arctan(y)]^0_n$
But now I'm stuck, can someone help me out?
2026-04-05 18:24:15.1775413455
Improper integral with two infinite bounds
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Observe the integrand is an even function, thus: $I = 2\displaystyle \int_{0}^\infty \dfrac{dy}{1+y^2} = 2\tan^{-1} y|_{y=0}^\infty = \pi$