Consider the function F(s)=s+8s3−3s2+3s−1F(s)=s+8s3−3s2+3s−1.

- Find the partial fraction decomposition of F(s)F(s):

s+8s3−3s2+3s−1=s+8s3−3s2+3s−1= +

- Find the inverse Laplace transform of F(s)F(s).

f(t)=L−1{F(s)}=f(t)=L−1{F(s)}=

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General GuidanceThe answer provided below has been developed in a clear step by step manner.Step: 1\begin{aligned}\frac{s+8}{s^{3}-3 s^{2}+3 s-1} & =\frac{s+8}{(s-1)^{3}} \\& =\frac{(s-1)}{(s-1)^{3}}+\frac{9}{(s-1)^{3}} \\\frac{s+8}{(s-1)^{3}} & =\frac{1}{(s-1)^{2}}+\frac{9}{(s-1)^{3}}\end{aligned}How taking laplace transformationL^{-1}\left(\frac{s+8}{(s-1)^{3}}\right)=L^{\prime}\left(\frac{1}{(s-1)^{2}}\right)+9 l^{-1}\left(\frac{1}{(s-1)^{3}}\right)secound shifting theoram\begin{array}{l}=e^{t} L^{-1}\left(\frac{1}{s^{2}}\right)+9 e^{t} \tau^{\prime}\left(\frac{1}{s^{3}}\right) \\=t e^{t}+\frac{9}{2} t^{2} e^{t}\end{array}=e^{t}\left(t^{2}+\frac{9}{2} t^{2}\right)Explanation:Please refer to solution in this step.Answer:this is required solution ...