Not sure how to start this question -.-
Find the Laplace transform of the function:
f(t)=te^(2t)cos(2t)
f(t)= ?
Thanks for the help!!
Hi there, been a while since i've done one of these, the definition is
$\displaystyle \mathcal{L}\left\{f(t)\right\}=\int_0^\infty e^{-st}f(t)~dt
$
Therefore
$\displaystyle \mathcal{L}\left\{te^{2t}cos(2t)
\right\}=\int_0^\infty e^{-st}te^{2t}\cos(2t)~dt=\int_0^\infty e^{t(2-s)}t\cos(2t)~dt
$
Also by the shift theorem
$\displaystyle \mathcal{L}\left\{e^{2t}\cos(2t)\right\}=\frac{s-2}{(s-2)^2+4}$