Final answer:
To find the inverse Laplace transform of F(s) given in partial fraction form, factoring the denominator and solving for the constants is necessary.
Step-by-step explanation:
The inverse Laplace transform of the given function F(s) can be found using partial fraction decomposition. First, factorize the denominator (s+1)(s+4)² as (s+1) and (s+4)². Then, express F(s) in partial fraction form as A/(s+1) + B/(s+4) + C/(s+4)². Next, solve for the values of A, B, and C by equating like terms. Finally, use the inverse Laplace transform tables to determine the inverse transform of each term separately.