# Inverse Laplace Transformation of arctan (s/2)

1. Nov 9, 2012

### nileszoso

The Title pretty much says it all. I'm trying to learn how to solve the Inverse Laplace Transformation of Arctan(s/2). An equation of this sort was not explicitly covered in class and I'm having difficulty figuring where to start to solve it. If anyone could give me a general idea that would point me in the right direction that would be greatly appreciated.

2. Nov 9, 2012

### keyns

The derivative of arctan(t)=1/(t^2+1). Differentiation in time-domain is the same as multiplication by s in Laplace-domain. See http://en.wikipedia.org/wiki/Laplace_transform for a table. You should be able to derive the correct answer from this.

3. Nov 10, 2012

### nileszoso

Thank you! This helped, although I'm still not sure what exactly is meant by "Differentiation in time-domain is the same as multiplication by s in Laplace-domain. " But like I said this got my started on the way to solve the problem.

4. Nov 18, 2012

### JJacquelin

Hi nileszoso!

A classical method to compute the inverse Laplace transform is the use of the Bromwich integral. In the case of arctan(s/2) this leads to ardous calculus with special functions.
Moreover, the inverse Laplace Transform of arctan(s) doesn't appears in some extended tables. So, it is questionable whether there is really a solution which can be expressed with not too complicated combinations of standard functions.
Where this problem is coming from ?