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I need some explanation here. I got the solution but I don't understand something.

Question:

Find the integral using Residue Theorem.

$$\int_{-\infty}^{\infty}\frac{dx}{(x^2+4)^2}$$

Here is the first part of the solution that I don't understand:

To evaluate ##\int_{-\infty}^{\infty}\frac{dx}{(x^2+4)^2}##, consider ##\oint_c\frac{dz}{(z^2 + 4)^2}##,

where C consists of the real axis [-R, R] with R > 2, and the upper half of Γ: |z| = R (all with counterclockwise orientation).

My question: Why is R>2?