Question

How do you use partial fraction decomposition to decompose the fraction to integrate `(x^2-4)^-1`?

Answer 1

`(x^2-4)^-1 is 1/(x^2-4)`

Its partial fraction would be `1/4[1/(x-2) -1/(x+2)]`

Integration would give `1/4[ln(x-2) -ln(x+2)}`

=`1/4 ln((x-2)/(x+2))`