$\begin{aligned} & \text { Let } I=\int \frac{d x}{x^2 \sqrt{4+x^2}} \\ &=\int \frac{d x}{x^3 \sqrt{\frac{4}{x^2}+1}} \\ & \text { Put } \quad \frac{4}{x^2}+1=t \\ & \Rightarrow \quad-\frac{8}{x^3} d x=d t \\ & \therefore \quad I=\int \frac{d t}{-8 \sqrt{t}} \\ &=-\frac{1}{8} \times \frac{\sqrt{l}}{1 / 2}+C \\ &=-\frac{1}{4} \sqrt{\frac{4}{x^2}+1}+C \\ &=-\frac{1}{4 x} \sqrt{4+x^2}+C\end{aligned}$