Find the surface integral of some ellipsoid?

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I got Stokes theorem all warmed up for this one!

$$\int_{S}\int(Curl(\vec{F}))d\vec{s}$$ (That means delta cross F or curl of F) Where S is the ellipsoid $x^2 + y^2 + 2z^2 = 16$

And $\vec{F} = sinxy\vec{i} +e^x\vec{j} - yz\vec{k}$

Where do I move from here?

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Hint: Notice that the surface $S$ has no boundary, so that applying Stokes here results in integrating over the empty set.