-4 square root x/2
Until today I was under the impression that even in North Carolina the freedom of speech was guaranteed. Obviously I am mistaken ...
After polishing my crystal sphere I assume that you want to determine
$\displaystyle \displaystyle{\int \left(-4 \cdot \sqrt{\frac x2} \right) dx}$
or
$\displaystyle \displaystyle{\int \left(-4 \cdot \frac{\sqrt{ x}}2 \right) dx}$
Which one do you want to do and where are your difficulties that you can't proceed?
$\displaystyle \begin{align*}\displaystyle{\int \left(-4 \cdot \sqrt{\frac x2} \right) dx} =& \frac{(-8)\cdot(x)^{\frac{3}{2}}}{3\sqrt{2}} + C \\ =& \frac{-4\sqrt{2}\cdot(x)^{\frac{3}{2}}}{3} + C\end{align*}$
You can check the answer:
int -4 (x/2)^(1/2) - Wolfram|Alpha