Textbook Problem

Dialysis treatment removes urea and other waste products from a patient’s blood by diverting some of the bloodflow externally through a machine called a dialyzer. The rate at which urea is removed from the blood (in mg/min) is often well described by the equation

$u\left(t\right)=\frac{r}{\text{V}}{C}_0{e}^{-rt/V}$

where r is the rate of flow of blood through the dialyzer (in mL/min), V is the volume of the patient’s blood (in mL), and $C_0$ is the amount of urea in the blood (in mg) at time $t=0$. Evaluate the integral ${\displaystyle {\int }_0^{\infty }u\left(t\right)}$ and interpret it.