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Homework 12 (MATH 1199 Fall 2019)
1. Compute the improper integral using the residue theorem:

$\displaystyle\int_{-\infty}^{\infty} \dfrac{3}{x^2+5} \mathrm{d}x.$

2. Compute the improper integral using the residue theorem:

$\displaystyle\int_0^{\infty} \dfrac{2x^2+1}{x^4+1} \mathrm{d}x.$