1. ## Anti derivative

-4 square root x/2

2. ## Re: Anti derivative

-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?

3. ## Re: Anti derivative

The first one. I know that when its square root of x it can become x^1/2 but what about when it's square root of x/2. What's the anti derivative

4. ## Re: Anti derivative

Hint: $\displaystyle \sqrt{\frac{x}{2}}=\frac{\sqrt{x}}{\sqrt{2}}$.

5. ## Re: Anti derivative

\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*}