Answer to Question #343127 in Differential Equations for Tobias Felix

Question #343127

Find the Laplace transforms of the following function:

9. L{7t^3 - 2sin3t}


1
Expert's answer
2022-05-23T16:06:20-0400
"{\\cal L}\\{f\\}(s)=\\int_0^{\\infty}f(t)e^{-st}dt""{\\cal L}\\{7t^3-2\\sin3t\\}(s)\\\\\n=7\\int_0^{\\infty}t^3e^{-st}dt-2\\int_0^{\\infty}\\sin3te^{-st}dt\\\\\n=7*\\frac{3!}{s^4}-2*\\frac{3}{9+s^2}\\\\\n=\\frac{42}{s^4}-\\frac{6}{9+s^2}"

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