A research probe measures the rate of accumulation of cosmic dust, DDD, on a satellite's surface over time, ttt, in years. The rate is modelled by the function:
dDdt=58t4−27t5+3 \frac{dD}{dt} = \frac{5}{8}t^4 - \frac{2}{7t^5} + \sqrt{3} dtdD=85t4−7t52+3Find the general expression for D(t)D(t)D(t) by evaluating:
∫(58t4−27t5+3)dt \int \left( \frac{5}{8}t^4 - \frac{2}{7t^5} + \sqrt{3} \right) dt ∫(85t4−7t52+3)dtsimplifying your answer.
