Answer to Question #343127 in Differential Equations for Tobias Felix

Question

Find the Laplace transforms of the following function:

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

Answer 1

$${\cal L}\{f\}(s)=\int_0^{\infty}f(t)e^{-st}dt$$ $${\cal L}\{7t^3-2\sin3t\}(s)\\ =7\int_0^{\infty}t^3e^{-st}dt-2\int_0^{\infty}\sin3te^{-st}dt\\ =7*\frac{3!}{s^4}-2*\frac{3}{9+s^2}\\ =\frac{42}{s^4}-\frac{6}{9+s^2}$$