Find the volume under the given surface $z=f(x, y)$ and above the rectangle with the given boundaries.

$$z=x \sqrt{x^{2}+y} ; \quad 0 \leq x \leq 1,0 \leq y \leq 1$$

$\frac{2}{15}\left(2^{5 / 2}-2\right)$ cubic units.

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