So I know what $E[X^2]$ and $E[X^4]$ are and I need the first moment. Would it be a right approach for me to use the equality below
$$E[X^4] - E[X^2] = (E[X^2] - E[X^1])\times(E[X^2] + E[X^1])$$
If not is there another way to find the first moment using these two? I have the function but integrating is kinda tough so I am trying to avoid it.
It's not possible to know $E[X]$ only from $E[X^2]$ and $E[X^4]$. For instance, if you have $Y=-X$, then $E[Y^2]=E[X^2]$ and $E[Y^4]=E[X^4]$, but $E[Y]=-E[X]$.