I've learned a couple of methods of integrating, but I'm still not sure when to use which one.

Example problem is 
\begin{align}
\int x^3\sin x^2\,dx
\end{align}
I tried using a method where I set something to $u$ and $dv$ and go from there, but I don't end up anywhere with this problem. I know you can use substitution method and then integrate by parts, but I'm not sure which part of the integral I should begin substituting.