Originally Posted by

**topsquark** Evaluate

$\displaystyle \displaystyle \int \frac{dy}{1 - y^2}$

There are essentially two ways to approach this. The first is

$\displaystyle \displaystyle \int \frac{dy}{1 - y^2} = tanh^{-1}(y) + C$

The other is to use partial fractions:

$\displaystyle \displaystyle \int \frac{dy}{1 - y^2} = \frac{1}{2} ln \left | \frac{1 + y}{1 - y} \right | + C$

Now, tanh^(-1) and ln have an overlapping domain and in this region everything is just fine and C = 0. The problem is that the ln solution has a much larger domain than the tanh one.

How can two solutions of an integral have different domains?

-Dan