Question

Find the Laplace transforms of the following function:

6. L{2cos3t + 5sin3t}

Answer 1

$${\cal L}\{f\}(s)=\int_0^{\infty}f(t)e^{-st}dt$$ $${\cal L}\{2\cos3t+5\sin3t\}(s)\\ =2\int_0^{\infty}\cos3te^{-st}dt+5\int_0^{\infty}\sin3te^{-st}dt\\ =2*\frac{s}{9+s^2}+5*\frac{3}{9+s^2}\\ =\frac{2s}{9+s^2}+\frac{15}{9+s^2}$$