Answer
$$ \displaystyle\int \sqrt{x{\cdot}\left(4-x\right)}\, \mathrm d x = {{x\,\sqrt{-\left(x-4\right)\,x}-2\,\sqrt{-\left(x-4\right)\,x}+4\, \arcsin \left({{x-2}\over{2}}\right)}\over{2}} $$
Explanation
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