## integrating kinetice energy eqn

Hi all,

I'm inquiring as to the steps involved in determining head loss equation from following kinetic energy work done equality.
$\frac{d}{dt}$ ( $\frac{1}{2}$ $LU^2)$ = - $\frac{1}{2}$ $\ n C D L U^3$

I'm looking for the methodology to determine the velocity U as a function of x, the distance traveled. the following chain rule relation is used
$\frac{du}{dx}$ = $\frac{1}{U}$ $\frac{dU}{dt}$

Integrating with respect to x yields the following equality
$\frac{U}{U_0}$ = exp(- $\frac{n C D x}{2})$

Can anyone help me with the steps involved in going from the first equation to the final equality