$\int\frac{x^2}{\left(4x^2+12\right)^3}dx$

$\frac{\sqrt{3}}{576}\left(\frac{1}{2}\arctan\left(\frac{2x}{\sqrt{12}}\right)+\frac{\sqrt{12}x}{4x^2+12}\right)+\frac{-\sqrt{12}\sqrt{3}x}{768\left(4x^2+12\right)}+\frac{-\sqrt{3}\arctan\left(\frac{2x}{\sqrt{12}}\right)}{1536}+\frac{-\sqrt{\left(12\right)^{3}}\sqrt{3}x}{1152\left(4x^2+12\right)^{2}}+C_0$