I missed a class this week in maths and been a bit lost since with Inverse Laplace, how do I go about finding the Inverse laplace of: $$\frac{(s+1)^3}{s^4}$$
Do I simply expand the numerator? then inverse laplace? or is there a quicker way of doing it, expanding the brackets seems like a lengthy process...if someone could help me I'd be grateful as I have a test on this Friday!
$$\frac{(s+1)^3}{s^4} = \frac 1s + \frac 3{s^2} + \frac 3{s^3} + \frac 1{s^4}$$ and the inverse Laplace transform of each of those terms should be standard to you. After you've found it, it may be possible to simplify the answer!
(If the inverse transform of these terms are not in your head, go back to your notes, text or this nice MIT lecture on the topic: http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-19-introduction-to-the-laplace-transform/ )