Int t^3/(2-t^2) ^(5/2) dt

$\int \frac{t^3} {(2-t^2)^{5/2} } dt$
Was going to expand
$$\frac{2t}{\left(2-{t}^{2} \right)^{5 /2 } }
-\frac{t}{\left(2-t^2 \right)^{3/2 } }$$