Cual es la transformada inversa de la siguiente función: (S^2-2S+1)/(S(S^3+9S))

Vamos a encontrar la transformada inversa de la siguiente función de Laplace:

\[
F(s) = \frac{s^2 - 2s + 1}{s(s^3 + 9s)}
\]

### Paso 1: Simplificar la expresión

Podemos factorizar el denominador de la función:

\[
s(s^3 + 9s) = s(s(s^2 + 9)) = s^2(s^2 + 9)
\]

Entonces, la función

Find the inverse Laplace transform of the function (S^2-2S+1)/(S(S^3+9S)) with a detailed step-by-step solution. This problem covers key topics in Laplace transforms, including algebraic factorization and partial fraction decomposition. Suitable for university-level students.

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