Determine whether the integral $\displaystyle {\int_{{2}}^{\infty}}\frac{{{x}^{{2}}+{3}}}{{{x}^{{4}}+{9}{x}^{{2}}+{29}}}{\left.{d}{x}\right.}$ is divergent or convergent.
Use a comparison of $\displaystyle {\int_{{2}}^{\infty}}\frac{{{x}^{{2}}+{3}}}{{{x}^{{4}}+{9}{x}^{{2}}+{29}}}{\left.{d}{x}\right.}$ to $\displaystyle \int\frac{{\left.{d}{x}\right.}}{{x}^{{p}}}$ for a positive integer p.
Smallest p =
$\displaystyle {\int_{{2}}^{\infty}}\frac{{\left.{d}{x}\right.}}{{x}^{{p}}}$ <     > $\displaystyle {\int_{{2}}^{\infty}}\frac{{{x}^{{2}}+{3}}}{{{x}^{{4}}+{9}{x}^{{2}}+{29}}}{\left.{d}{x}\right.}$
$\displaystyle {\int_{{2}}^{\infty}}\frac{{\left.{d}{x}\right.}}{{x}^{{p}}}$ convergesdiverges.
So $\displaystyle {\int_{{2}}^{\infty}}\frac{{{x}^{{2}}+{3}}}{{{x}^{{4}}+{9}{x}^{{2}}+{29}}}{\left.{d}{x}\right.}$ convergesdiverges