How is it possible to recover $\displaystyle u(x)$ given the its fourier transform $\displaystyle v(\omega)$ and the inverse transform? by using the definition?

$\displaystyle v(\omega) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{-iwx}{u(x)}{dx}$

$\displaystyle u(x) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{iwx}{v(\omega)}{d\omega}$

is there some sort of change of variables that needs to be done?

Thanks