If

f(s) = script l{f(t)}

and

n = 1, 2, 3, . . ,

thenscript l{tnf(t)} = (−1)n

dn
dsn
f(s).

evaluate the given laplace transform. (write your answer as a function of s.)

script l{t cos 5t}

Step-by-step explanation:

Let's use the definition of the Laplace transform and the identity given: with .

Now, . Using integration by parts with u=e^(-st) and dv=cos(5t), we obtain that .

Using integration by parts again with u=e^(-st) and dv=sin(5t), we obtain that

.

Solving for F(s) on the last equation, , then the Laplace transform we were searching is

5

step-by-step explanation: