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.
Best Answer
Hint:
Setting $t=x^2\,\Rightarrow\, dt=2x\,dx$, then we have \begin{align} \int x^3\sin x^2\,dx=\frac{1}{2}\int t\,\sin t\,dt \end{align} Now apply integration by part by taking $u=t$ and $dv=\sin t\,dt$.