Final answer:
The inverse Laplace transform of f2(s) involves partial fraction decomposition and applying known transforms to find a sum of exponential and polynomial terms in t.
Step-by-step explanation:
The inverse Laplace transform of the function f2(s) = \frac{5s+2}{(s+1)(s+2)^2} is found using partial fraction decomposition and then utilizing known inverse Laplace transforms from a table or general knowledge. The function can be decomposed into simpler fractions that can easily be inverted. For example, A/(s+1) and (Bs+C)/(s+2)^2, where A, B, and C are constants to be determined. After finding these constants, the inverse Laplace transform is applied to each individual term leading to a solution which is a sum of exponential and polynomial terms in t, each term representing a specific behavior of the system over time.