La place transform!?

Question

L { integral from 1 to t (xe^-x dx) }...
find F(s)

Answer 1

Integrating first,
let u = x, du = dx
dv = e^-xdx, v = - e^-x
giving
-xe^-x + ∫e^-xdx =
-(x + 1)e^-x
applying limits,
-(t + 1)e^-t + 1 =
1 - e^-t - te^-t
Applying the transforms,
1/s - 1/(s + 1) - 1/(s + 1)^2

Answer 2

Don't you have a transform pair table? I don't remember it off the top of my head (is it s or s² or 1/s) and my LaPlace Transform reference isn't here (it's in my office). Find it on the web.


Doug

Answer 3

(-t-1)(e^-t) +2/e is the integral, idk the rest is what sry

Answer 4

tricky shtuff
i dunno