# Inverse laplace transform

## Main Question or Discussion Point

Hi all,

I'm struggling to find the inverse Laplace transform of the following function:

F(s) = (1+ 4exp(-s) - 5exp(-3s)) / s(s^2 + 11s + 55)

Any help is appreciated.

Thanks

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chiro
Hi all,

I'm struggling to find the inverse Laplace transform of the following function:

F(s) = (1+ 4exp(-s) - 5exp(-3s)) / s(s^2 + 11s + 55)

Any help is appreciated.

Thanks
Hey guava91011 and welcome to the forums.

From looking at that you could separate it into terms by decomposing the fraction by terms in the numerator and then use convolution theorems and completing the square. Try completing the square for s^2 + 11s + 55 and consider that e^(-ap)/p is the Laplace form for the Heaviside (and e^(-ap) is for dirac delta).

You can also use the other standard properties like shift theorem and so on.

Please show your working and whatever you have tried so that people here can give you some help that will actually help you instead of help that will just get through the question without any understanding.