What is the inverse Laplace transform of F(s) = (s + 1)/(s^2 + 1)^2

[interxavier]

Homework Statement

F(s) = (s + 1)/(s² + 1)²

Homework Equations

The Attempt at a Solution

I used partial fractions but I still end up with a term that includes a (s^2 + 1)^2 in the denominator. I'm pretty much lost at this point.

 

[fzero]

You could try writing the inverse transform as a convolution. I think you can compute the integral by using trig identities.

 

[mikeleeds]

Partial fractions won't work (as you've found), split it up into two bits and then use a table of Laplace transforms to work backwards, they are standard results - unless you're being made to there is no point in trying the integration yourself

 

[vela]

The form of the denominator suggests F(s) can be expressed in terms of the derivatives (with respect to s) of the Laplace transforms for sine and cosine. You can try futzing around with those to see if you can combine them the right way. You might find it helpful to use

\frac{s^2}{(s^2+1)^2} = s\left[\frac{s}{(s^2+1)^2}\right]

in combination with one of the properties of Laplace transforms.

If you're familiar with complex analysis, the most straightforward way to me would be to evaluate the inverse Laplace transform integral since you have only two poles to worry about.