\[
\int {\frac{{x^2 }}{{\left( {x^2  + a^2 } \right)^2 }}dx}  =  - \frac{1}{2}\frac{x}{{x^2  + a^2 }} + \frac{1}{{2a}}{\mathop{\rm arctg}\nolimits} \frac{x}{a}
\]