It is the Jacobian which appears in the density. Really there should be some $\text{d}u$ terms to make it clearer that it is not the probability distribution function.
What's a good reference for this derivation (online).? Wikipedia only has an advertisement for someone's book as a reference.
I find this presentation very confusing, for example I had been missing that this was the density (small c) as opposed to the CDF and was obviousobviously not making any sense of it. I can imagine other readers doing the same thing.