Final answer:
The question asks for the partial fraction decomposition of F(s)= 2s+5/(s^3 -3s^2 +3s-1). The general approach would involve factoring the cubic polynomial in the denominator into simpler linear or quadratic factors. However, without the specific factors, a detailed decomposition cannot be given.
Step-by-step explanation:
To find the partial fraction decomposition of the function F(s) = \frac{2s+5}{s^3 - 3s^2 + 3s - 1}, we first need to factor the denominator, if possible. Unfortunately, the given information from Solution 13.4 does not seem to aid in finding the partial fraction decomposition directly. However, the general approach involves expressing the function as a sum of simpler fractions, each with a simpler denominator.
The denominator is a cubic polynomial, and if it can be factored into linear factors, then the partial fraction decomposition can be written as:
A/(s - a) + B/(s - b) + C/(s - c) where a, b, and c are the roots of the cubic polynomial.
If the cubic polynomial cannot be factored into linear factors using real numbers, it is possible that complex roots are involved, and different techniques might be required, potentially involving quadratic factors in the denominator. In such cases, without knowing the specific factors of the cubic polynomial, a step-by-step decomposition cannot be provided.
It is worth noting that partial fraction decomposition is a technique used to simplify complex rational expressions, especially useful when integrating such functions.