What is the inverse Laplace transform of F(s) = (s+1)/(s^2 + 4s + 5)?

a) e^(-t) sin(t)
b) e^(-t) cos(t)
c) e^(-t/2) sin(t/2)
d) e^(-t/2) cos(t/2)

Answer: d) e^(-t/2) cos(t/2)

Explanation: We can use partial fraction decomposition and the inverse Laplace transform tables to find the solution. After partial fraction decomposition, we get F(s) = (s+1)/(s^2 + 4s + 5) = (s+1)/[(s+2)^2 + 1]. Using the inverse Laplace transform table, we find that the inverse Laplace transform of (s+1)/[(s+2)^2 + 1] is e^(-at) cos(bt), where a = -2 and b = 1. Therefore, the answer is d) e^(-t/2) cos(t/2).

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