Find the inverse laplace transforms, as a function of x, of the following functions:
2s^2/ (s – 1)(s^2 +1)

 The required answer is

Step-by-step explanation:  We are given to find the inverse Laplace transform of the following function as a function of x :

We will be using the following formulas of inverse Laplace transform :

By partial fractions, we have

where A, B and C are constants.

Multiplying both sides of the above equation by the denominator of the left hand side, we get

If s = 1, we get

Also,

Comparing the coefficients of x² and 1, we get

So, we can write

Taking inverse Laplace transform on both sides of the above, we get

Thus, the required answer is

step-by-step explanation:

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