Question

Find the inverse Laplace transform of
F(s)=s+2/(s²+6 s+11)(s-1) .

Answer 1

To find the inverse Laplace transform of the given function F(s), we can use partial fraction decomposition and the Laplace transform table.

Step-by-step explanation:

The inverse Laplace transform of the given function F(s) can be found using partial fraction decomposition and the Laplace transform table. First, we need to factorize the denominator (s² + 6s + 11)(s - 1) using the quadratic formula. The two roots of the quadratic equation are -3 + 2i and -3 - 2i. Using partial fraction decomposition, we can express F(s) as:

F(s) = A/(s + 3 + 2i) + B/(s + 3 - 2i) + C/(s - 1)

In order to find the constants A, B, and C, we can multiply both sides of the equation by the denominator and then substitute values that make the other terms zero. Once we have the values of A, B, and C, we can use the Laplace transform table to find the inverse Laplace transform of each term.