1. Integration Problem

I need to find the indefinite integral of:
$\displaystyle \sqrt[3]{xe}^{\sqrt[3]{8x^4}}dx$

$\displaystyle \sqrt[3]{xe}^{\sqrt[3]{8x^4}}dx$
Is that actually a third root to the [\sqrt[3]{8x^4}[/tex] power? Then it is simply $\displaystyle \left(x e\right)^{2^{1/3}x^{4/3}}$. Are you sure that is not a product rather than a power?