Solve ∫ wrt x/(x^2+a^2)^3dx

$$\int \frac { d x } { ( x ^ { 2 } + a ^ { 2 } ) ^ { 3 } } d x$$

Evaluate

$$\left\{\begin{matrix}\frac{dx\left(32С+\frac{\left(\sin(4\arctan(\frac{x}{|a|}))+8\sin(2\arctan(\frac{x}{|a|}))+12\arctan(\frac{x}{|a|})\right)|a|}{a^{6}}\right)}{32},&a\neq 0\\Сdx-\frac{d}{5x^{4}},&a=0\end{matrix}\right.$$

Differentiate w.r.t. x

$$\left\{\begin{matrix}\frac{d\left(32С+\frac{\sin(4\arctan(\frac{x}{|a|}))|a|a^{2}+\sin(4\arctan(\frac{x}{|a|}))|a|x^{2}+8\sin(2\arctan(\frac{x}{|a|}))|a|a^{2}+8\sin(2\arctan(\frac{x}{|a|}))|a|x^{2}+4\cos(4\arctan(\frac{x}{|a|}))xa^{2}+12\arctan(\frac{x}{|a|})|a|a^{2}+12\arctan(\frac{x}{|a|})|a|x^{2}+16\cos(2\arctan(\frac{x}{|a|}))xa^{2}+12xa^{2}}{\left(x^{2}+a^{2}\right)a^{6}}\right)}{32},&a\neq 0\\Сd+\frac{4d}{5x^{5}},&a=0\end{matrix}\right.$$