A laboratory technician models the rate of change of the volume, VVV, of a liquid in a cooling system. The model used is
dVdt=5t2+46t3,t>0 \frac{dV}{dt} = \frac{5t^2 + 4}{6t^3}, \quad t > 0 dtdV=6t35t2+4,t>0where ttt is the time in hours. Determine the general expression for VVV in terms of ttt, giving your answer in simplest form.