<s>[INST] Calculating integral I need some help to solve this integral:
$$\int(x^2+y^2)^{-\frac32} \mathrm dx$$ 
Thank you. 
 [/INST] Put $x = y \tan t$ and $dx = y \sec^2 t\ dt$, then
$$
\begin{align}
\int\frac{dx}{\sqrt{(x^2+y^2)^3}}&=\int\frac{y \sec^2 t\ dt}{\sqrt{(y^2\tan^2 t+y^2)^3}}\\
&=\int\frac{y \sec^2 t\ dt}{y^3\sec^3 t}\\
&=\frac{1}{y^2}\int\cos t\ dt\\
&=\frac{\sin t}{y^2}+C\\
&=\frac{x}{y^2\sqrt{x^2+y^2}}+C.
\end{align}
$$
</s>