Inverse Laplace Transformation of Inverse Tan function

[annamation]

Homework Statement

Take the Inverse Laplace Transform of F(s) where
F(s)=((s)(tan-1(1/s)))

Homework Equations

The Attempt at a Solution

i know that f(t)=L-1(F(s))=(-1/t)L-1(F'(s))
and d/ds(1/tan-1(x))=1/x^2 +1
but the example I'm given with an inverse laplace of tan-1 is way prettier than this problem. hint?

 

[foxjwill]

Well, the first thing to note is that

$$\tan^{-1}\left(\frac{1}{s}\right)=\cot^{-1}{(s)}.$$​

Do you know the convolution theorem?

Also, if you're not going to use latex, please use the "sup" and "sub" buttons (they're the buttons that look like $$\text{X}^2$$ and $$\text{X}_2$$). And make sure you use parentheses for the denominators of fractions. That said, I highly recommend you learn at least some basic latex. It's not very difficult.