Find the integral of g(x) = (x-2)/(x^2-4)

Given that g(x) =
(x-2)/(x^2-4)

We need to find the integral of
g(x).

First we will
simplify.

g(x) = (x-2)/(x-2)(x+2) =
1/(x+2)

==> g(x) =
(x+2)^-1

Now we will
integrate.

==> Intg g(x) dx = Int (x+2)^-1
dx

We will assume that u= x+2 ==> du =
dx

==> Int g(x) dx = Int 1/u du = ln u +
c

Now we will substitute back u=
x+2

==> Int g(x) = ln (x+2) +
C