Tìm nguyên hàm $\int{{\frac{x}{{{{x}^{2}}+1}}dx}}.$
A. $\displaystyle \frac{1}{2}\ln \left| {{{x}^{2}}+1} \right|+C.$
B. $\frac{{-2}}{{{{{\left( {{{x}^{2}}+1} \right)}}^{2}}}}+C.$
C. $\frac{2}{{{{{\left( {{{x}^{2}}+1} \right)}}^{2}}}}+C.$
D. $\displaystyle -\frac{1}{2}\ln \left| {{{x}^{2}}+1} \right|+C.$