Hi,
I'm working through an example of using residues to evaluate an improper integral, but I don't see how they arrive at the following initial step:
x^2 / ((x^2 + 1)(x^2 +4)) = 1/3[ (4 / (x^2 + 1) - (1 / (x^2 + 4)]
Any help would be appreciated
Thanks
That initial step just consists of using partial fractions to write , for suitable constants A and B. (If that looks odd, replace by a single variable, say , to make it look more like a standard partial fractions decomposition.)
Why the worked example ahould have started in this way is a bit of a mystery. As Mr F points out, the way to solve the problem is to use the residue theorem, and it doesn't seem necessary to use partial fractions in order to find the residues.