Laplace & Inverse Laplace Transforms

[2RIP]

Homework Statement

L[f(t)]= 1/(s^2+1)^2 + 1/(s^2+1)
L[f(t)]= ln(s+a) where 'a' is a constant

Homework Equations

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]

Homework Statement

L[f(t)]= 1/(s^2+1)^2 + 1/(s^2+1)
L[f(t)]= ln(s+a) where 'a' is a constant

Homework Equations

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

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