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The Laplace transform of a function (f(t)) is defined as: [ \mathcal{L}{f(t)} = \int_0^\infty f(t) e^{-st} , dt ] For (f(t) = t^2 e^{2t}), we have: [ \mathcal{L}{t^2 __________ ________ ________ ___ _________ _______ ___ ____ __________ ___ ___ ______.
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