#1**+2 **

*"how do you find the inverse Laplace transform of 5/(s-1)(s2+4)"*

Assuming the function of interest is \(f(s)=\frac{5}{(s+1)(s^2+4)}\)

First expand as partial fractions: \(f(s)=\frac{1}{s-1}-\frac{s}{s^2+4}-\frac{1}{s^2+4}\)

Then do the inverse Laplace transforms of these (the first term wil result in an exponential, the second will have the form of a cosine, and the third the form of a sine).

Alan Sep 19, 2019

#2**+1 **

Thanks for your help.

Can you recommend anything to help me expand as partial fractions, please?

Guest Sep 19, 2019

#3**+1 **

Try the following site: https://www.mathsisfun.com/algebra/partial-fractions.html

Incidentally, I’ve just noticed that in my original reply I had (s+1) in the denominator rather than (s-1). However, the same approach should be used, I.e. expand using partial fractions, then inverse Laplace each of the simpler fractions so obtained.

Alan
Sep 20, 2019