Find, in simplest form,
∫3(2x−5)4 dx \int \frac{3}{(2x - 5)^4} \, \mathrm{d}x ∫(2x−5)43dxA population of bacteria grows at a rate R(t)=82t+1\displaystyle R(t) = \frac{8}{2t + 1}R(t)=2t+18 million per hour, where t t\,t is the time in hours, t≥0t \ge 0t≥0.
Show, by algebraic integration, that the total growth in the population between t=1t = 1t=1 and t=3t = 3t=3 is lnb \ln b\,lnb million, where b b\,b is a rational constant to be found.
