Rydbirk,

On the right hand side, the integration is simple, with A being the constant of integration, so I imagine you're asking about what they did on the left hand side.

First, they used the fact that to get

Next, you use the method of partial fractions:

for some A, B.

To find A and B, we multiply this by to get:

Equating the coefficients of powers of v, we get and

This gives and . Thus:

Now, note that , so ,

,

and

Then you use the fact that to get

which is the left hand side of their result.

--Kevin C.