What's the integration of square root(2 x-1)/square root (2x+1)

I can solve all this with completing the square of
but what can I do with the Extension (I mean the upper part of fraction)- are there any way that I can drop the square root so it's solution will be easier

sqrt(2x - 1) / sqrt(2x + 1)
= [sqrt(2x - 1)sqrt(2x - 1)] / [sqrt(2x - 1)sqrt(2x + 1)]
= (2x - 1) / sq(4x^2 - 1)
= [2x / sqrt(4x^2 - 1)] - [1 / sqrt(4x^2 - 1)]

For the workings, look here:
http://www.wolframalpha.com/input/?i=int…

The final solution is not easier though.

Multiply the denominator by its conjugate √(2x - 1). That means you'll integrate (2x - 1) / √(4x^2 - 1) where you'll let u = 4x^2 - 1, and du = 8x dx.