Need help compute the laplace transform

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need help
compute the laplace transform of
h(t)= -5t^2
I took the integral((-5t^2)e^-(st)) i forgot integration by parts so i did it the hard way in my head and finally got
lim t -> oo 5[(-1/s)(t^2)(e^-st) - (2te^-st) - (2se^-st)] 0--oo
i got 10s but the book says -10/s^3
did i get the inetgration wrong or is it the second part thats wrong

i also have to verify that L[t^n]= n!/s^(n+1) basicaly the same problem but general
muchos gracias and stuff
 

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  • #2
saltydog
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[tex]\mathcal{L}\{-5t^2\}=-5\int_0^\infty e^{-st}t^2 dt[/tex]

Let:

[tex]u=t^2[/tex]

[tex]dv=e^{-st}dt[/tex]

Really need to use parts for this. Also, this is a standard one that most ODE books will illustrate.
 

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