Find

$$\int \frac{(3w+2{)}^2}{4\sqrt{w}}dw,w>0$$

giving your answer in simplest form.

The concentration $C$ of a chemical in a solution, measured in mol/L, changes over time $t$ seconds according to the model $C=f(t)$.

It is given that:

• $f^{\prime }(t)=t^2+kt+m$, where $k$ and $m$ are constants.
• The initial concentration of the chemical is 12 mol/L.
• At $t=3$, the concentration is 18 mol/L.
• At $t=3$, the rate of change of the concentration is 2 mol/L/s.

Find $f(t)$ in simplest form.