The rate at which a specific toxin accumulates in a filtration system, R(t)R(t)R(t) in mg per hour, is modeled for t≥0t \ge 0t≥0 by the function:
R(t)=2t4+11t3+16t2+15t+46(t+3)2 R(t) = \frac{2t^4 + 11t^3 + 16t^2 + 15t + 46}{(t+3)^2} R(t)=(t+3)22t4+11t3+16t2+15t+46Determine the values of the constants A,B,C,A, B, C,A,B,C, and DDD such that
R(t)=At2+Bt+C+D(t+3)2 R(t) = At^2 + Bt + C + \frac{D}{(t+3)^2} R(t)=At2+Bt+C+(t+3)2DHence find
∫R(t) dt \int R(t) \, dt ∫R(t)dt