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Find unilateral Laplace transform for the following signals, $ x(t)=u(t) $
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Solution:

$ X(S)=\int_0^{\infty} \mathrm{x}(\mathrm{t}) \mathrm{e}^{-\mathrm{st}} \mathrm{dt}\\ $

$ =\int_0^{\infty} \mathrm{u}(\mathrm{t}) \mathrm{e}^{-\mathrm{st}} \mathrm{dt}\\ $

$ \int_0^{\infty} 1 e^{-s t} d t=\left[\frac{e^{-s t}}{-s}\right]_0^{\infty}\\ $

$ =\left[\frac{e^{-s t}}{-s}\right]_0^{\infty}=\frac{1}{s}\\ $

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