Find real constants $A,B$ and $C$ and complex constants $D$ and $E$ such that

${\displaystyle \frac{10x^2-2x+4}{x^3+x}=\frac{A}{x}+\frac{\mathrm{Bx}+C}{x^2+1}=\frac{A}{x}+\frac{D}{x-i}+\frac{E}{x+i}.}$