Laplace & Inverse Laplace Transforms

2RIP

1. The problem statement, all variables and given/known data
L[f(t)]= 1/(s^2+1)^2 + 1/(s^2+1)
L[f(t)]= ln(s+a) where 'a' is a constant


2. Relevant equations



3. The attempt at a solution
I know that the inverse laplace of 1/(s^2+1) is sin(t), but how do I deal with the squared form of it.

I have never encountered a logarithmic funcion for laplace, so can it be inverted back to f(t) with some of the common solution of conversion?

Thanks

Mark44

For the first problem, and using a table of Laplace transforms, I see that:
L(1/(2w^2)(sin (wt) - wt cos(wt)) = 1/(s^2 + w^2)^2
and L(sin(wt)) = w/(s^2 + w^2)

I'm stumped on the other problem

HallsofIvy

No elementary function has ln(s+a) as its Laplace transform.

2RIP

f(t) = (-t)^n[f(t)]
F(s) = F(s)^nth derivative

I believe that's what I got to do for the second one. thanks