The rate of change of the volume of water, $V$, being pumped into a reservoir is modeled by the equation

$$\frac{dV}{dt}=\frac{7t^2}{4}-\frac{5}{2t^4}+\frac{2}{3}$$

where $V$ is measured in cubic metres and $t$ is the time in hours since pumping began. Determine the general expression for $V$ in terms of $t$, giving each term in its simplest form.