laplace transform help?

Question

can you help me find what the inverse laplace of the following is please ?

1/[s(s^2 + s + 1)] + s/(s^2 + s + 1) + 1/(s^2 + s + 1)

Answer 1

Get all three terms over a common denominator:

1/[s(s² + s + 1)] + s/(s² + s + 1) + 1/(s² + s + 1) = (1 + s² + s)/[s(s² + s + 1)] = 1/s.

So the inverse Laplace is 1.

This result could also be obtained by using partial fractions decomposition on the first term, but the above approach is easier.