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# Answer to Question #255905 in Electrical Engineering for Abubakar Tanveer

Question #255905

Find inverse Laplace transform of following:

1.F(s)=(S+1) / ((S+2)^2 (S+2S+4)^2 )

1
2021-10-25T07:34:03-0400

"L^{-1}\\left\\{\\frac{\\left(S+1\\right)}{\\left(\\left(S+2\\right)^2\\left(S+2S+4\\right)^2\\right)}\\right\\}\\\\\n=L^{-1}\\left\\{-\\frac{1}{2\\left(S+2\\right)}-\\frac{1}{4\\left(S+2\\right)^2}+\\frac{3}{2\\left(3S+4\\right)}-\\frac{3}{4\\left(3S+4\\right)^2}\\right\\}\\\\\n\\mathrm{Use\\:the\\:linearity\\:property\\:of\\:Inverse\\:Laplace\\:Transform:}\\\\\n\\mathrm{For\\:functions\\:}f\\left(s\\right),\\:g\\left(s\\right)\\mathrm{\\:and\\:constants\\:}a,\\:b:\\quad L^{-1}\\left\\{a\\cdot f\\left(s\\right)+b\\cdot g\\left(s\\right)\\right\\}=a\\cdot L^{-1}\\left\\{f\\left(s\\right)\\right\\}+b\\cdot L^{-1}\\left\\{g\\left(s\\right)\\right\\}\\\\\n=-\\frac{1}{2}e^{-2t}-\\frac{e^{-2t}t}{4}+\\frac{1}{2}e^{-\\frac{4t}{3}}-\\frac{e^{-\\frac{4t}{3}}t}{12}"

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