How do you set up this Tricky u-sub? Tricky u-sub.  Can you point me in the right direction?
$$\int{{x^3}\sqrt{5-2x^2}}dx$$
$u = 5-2x^2$
$ du = -4x dx$
Obviously, this does not match fully.

I tried breaking up the $x^3 = x*x^2$
 and I continued with:
$u=5-2x^2$
$2x^2 = 5-u$
$x^2=\frac{5-u}{2}$
But, I can't see how to make it all fit.
Am I on the right track?


Another approach:
We can write the integrand as
\begin{align*}
{x^3}\sqrt{5-2x^2}&=-\tfrac12x(5-2x^2)\sqrt{5-2x^2}+\tfrac52x\sqrt{5-2x^2}&&\text{then}\\[5pt]
\int{x^3}\sqrt{5-2x^2}dx&=-\frac12\int x\left(5-2x^2\right)^{3/2}dx+\frac52\int x\left(5-2x^2\right)^{1/2}dx\\[5pt]
&=\color{red}{\frac1{20}\left(5-2x^2\right)-\frac5{12}\left(5-2x^2\right)^{3/2}+C}
\end{align*}
