Question

laplace of f(t) = e^(3t) - 1/(t)

Answer 1

So I thought about splitting it up to: e^(3t)/(t) - 1/(t)

Answer 2

find the laplace of ea seperately?

Answer 3

i dont know how though

Answer 4

\[\int\limits_{0}^{\infty}f(x)e^{-sx}dx\]

Answer 5

do u know this property ?
\(\huge L[\frac{f(t)}{t}]= \int \limits_s^\infty F(s)ds\)

Answer 6

here f(t) = e^(3t) -1

Answer 7

okay but what is F(s)?

Answer 8

F(s) is the L.T of f(t)

Answer 9

okay sweet so i just take the integral and bam

Answer 10

yes, first find Laplace of f(t) = e^(3t) -1
and then take its integral from s to infinity

Answer 11

right

Answer 12

thats easy enough :) thanks :)

Answer 13

should i wait till you get the correct answer ?

Answer 14

wait whats the integral of 1/(s - 3) haha

Answer 15

ok, integral of 1/x dx is .... ?

Answer 16

ln(s - 3) ?

Answer 17

oh, yes :)

Answer 18

oh, duh (i need to stop second guessing my instincts) haha and so integral of 1/s is ln(s) too! :)

Answer 19

yes, avsolutely.

Answer 20

so what u get finally ?

Answer 21

isn't the answer just \[\frac{ 1 }{ s-3 }+1\]

Answer 22

no i got ln(s) - ln(s - 3) , s > 3

Answer 23

same as in the back of the book so i cant argue with that :)

Answer 24

yeah, correct, but that can be simplified to single log.

Answer 25

ln((s)/(s-3))

Answer 26

yes. :)