prove that $\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}\geq a+b+c$ 
If $a,b,c>0$, Then prove that $$\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}\geq a+b+c$$

$\bf{My\; Try::}$ Using Cauchy- Schwarz Inequality
$$\frac{a^4}{abc}+\frac{b^4}{abc}+\frac{c^4}{abc}\geq \frac{a^2+b^2+c^2}{3abc}$$
Now How can i solve after that , Help required, Thanks 

$$a^4+b^4+c^4\geq a^2bc+b^2ac+c^2 ab $$
holds by the rearrangement inequality or Muirhead's inequality.
