# Evaluate the integrals without using tables: \int_{-\infty}^{\infty}\frac{2x dx}{(x^{2}+1)^{2}}

The integrals converge. Evaluate the integrals without using tables.
$$\displaystyle{\int_{{-\infty}}^{{\infty}}}{\frac{{{2}{x}{\left.{d}{x}\right.}}}{{{\left({x}^{{{2}}}+{1}\right)}^{{{2}}}}}}$$

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Nathaniel Kramer
Given that