# I hope I created a quite clear Problem

Algebra Level 5

$f(x)=\sqrt{\dfrac{\left(4-\sqrt{x^2} \right) \left(\sqrt{x^2}+2 \right)}{ \left(10-\sqrt{x^2} \right) \left(\displaystyle \int_{0}^{\frac{\pi}{2}} \sin^9 \theta \ d\theta -\sqrt{x^2} \right)}}$

How many integral values of $$x$$ are included in the domain of the above real-valued function $$f(x)$$?

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