Solving the two integrals in the topic above using partial fractions gave the following result:
$$\int \frac{dZ}{Z^2-A^2} = \frac{1}{2A}\ln{\frac{Z-A}{Z+A}}+C.....eqn(1)$$
and
$$\int \frac{dZ}{A^2-Z^2} = \frac{1}{2A}\ln{\frac{A+Z}{A-Z}}+C.....eqn(2)$$
However I also noticed that I can express a relationship between the two integrals as thus:
$$\int \frac{dZ}{Z^2-A^2} = -\int \frac{dZ}{A^2-Z^2}.....eqn(3)$$
If the above eqn(3) is true, then it means we can further solve eqn(3) to give thus:
$$\int \frac{dZ}{Z^2-A^2} = -[\frac{1}{2A}\ln{\frac{A+Z}{A-Z}}+C_1] $$
Which simplifies into:
$$\int \frac{dZ}{Z^2-A^2} = \frac{1}{2A}\ln{\frac{A-Z}{A+Z}}+C].....eqn(4)$$
But looking at eqn(1) and eqn(4), they both appear to be different. What am I missing?