$\begin{align}  & \text{ }\int\limits_{-3}^{3}{\frac{x}{{{x}^{2}}+5}dx}=\frac{1}{2}\int\limits_{-3}^{3}{\frac{2x}{{{x}^{2}}+5}dx}=\left[ \frac{1}{2}{{\log }_{e}}({{x}^{2}}+5) \right]_{-3}^{3} \\ & \text{  }\int\limits_{-3}^{3}{\frac{x}{{{x}^{2}}+5}dx}=\frac{1}{2}\left[ \log ({{3}^{2}}+5)-\log ({{(-3)}^{2}}+5) \right] \\ & \text{  }\int\limits_{-3}^{3}{\frac{x}{{{x}^{2}}+5}dx}=\frac{1}{2}({{\log }_{e}}14-{{\log }_{e}}14)=0 \\\end{align}$