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Derive Laplace Transform of the Third Derivative
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[QUOTE="Curious3141, post: 4493152, member: 21250"] Start with ##L\{f(t)\} = \int_0^{\infty}e^{-st}f(t)dt##. Let ##u = f(t)## and ##dv = e^{-st}## and apply integration by parts. Solve for ##\int_0^{\infty} e^{-st}f'(t)dt##, which is ##L\{f'(t)\}##. There will be an ##f(0)## term in your expression. This is the standard method for finding the LT of a first derivative. Once you've done this, all you need to do is apply that iteratively (twice) to find the required LT of the third derivative. Note that you don't need to do the integration again, just apply the formula you've derived twice more. [/QUOTE]
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Derive Laplace Transform of the Third Derivative
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