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Question Number 173807 by mokys last updated on 18/Jul/22

Answered by aleks041103 last updated on 18/Jul/22

$$h\left(t\right)=\underset{0}{\stackrel{t}{\int }}f\left(x\right)g(t-x)dx$$$$histheconvolutionoffandg.$$$$forconvolutionandthelaplacetransform$$$${it}^{\prime }struethat:$$$$L\left[h\right]=L\left[f\right]L\left[g\right]$$$$\Rightarrow L\left[h\right]=\frac{s+2}{s^2+1}\frac{s^2+1}{(s+3)(s+2)}$$$$\Rightarrow L\left[h\right]\left(s\right)=\frac{1}{s+3}$$

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