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    Convolution Applied to Inverse Transform Problem

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    My problem lies in manipulating the equation to one which the inverse transform can be taken, but would appreciate this example of convolution worked with some more of the blanks filled. I cannot figure out how the equation
    gets manipulated into what appears to be .
    The main objective here is to find the inverse Laplace transform for h(s) using convolution.

    k and t are separate variables, not a single variable kt.

    Side Note: Is there a mathematical method for taking the inverse transform or are there just tables from people who did the original Laplace transform?

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    A convolution applied to an inverse Transform Problem. The solution is detailed and well presented. The solution received a rating of "5" from the student who posted the question.