Chapter 6.4, Problem 83E

Use Table 1 to evaluate all integrals involved in any solutions of Problems 71−94.

83. Marketing. After test marketing a new high-fiber cereal, the market research department of a major food producer estimates that monthly sales (in millions of dollars) will grow at the monthly rate of

     $S^{\prime }\left(t\right)=\frac{t^2}{{\left(1+t\right)}^2}$

t months after the cereal is introduced. If we assume 0 sales at the time the cereal is introduced, find S(t), the total sales t months after the cereal is introduced. Find the total sales during the first 2 years that the cereal is on the market.