Yes, that is strange, even with numerical parameters:
With[{a = 2, b = 1, x = 3},
Integrate[1/Sqrt[(x - u)^2 + v^2 + w^2],
{u, v, w} \[Element] Ellipsoid[{0, 0, 0}, {a, a, b}]]]
With a sphere the result is sensible, though:
With[{a = 1, b = 1, x = 3},
Integrate[1/Sqrt[(x - u)^2 + v^2 + w^2],
{u, v, w} \[Element] Ellipsoid[{0, 0, 0}, {a, a, b}]]]
