Yeah, I realized it was pretty stupid to integrate da/dt since I already had a(x). And I just used WolframAlpha to get coth(x/2), http://www.wolframalpha.com/input/?i=d%2Fdx%28cosh%28x%29-1%29*%281%2F%28d%2Fdx%28sinh%28x%29-x%29%29%29. It's probably just as easy to use sinh(x)/{cosh(x) -1}.
Now...
Peter Singer is an Australian philosopher/ethicist that has written a lot about this topic. Try looking up some of his articles, or get a hold of one of his books.
Given the following parametric form of the Friedmann Equation for an open, dust-filled (matter-dominated) universe:
a(x)={a_0 \Omega \over 2(1-\Omega)}(cosh(x)-1)
t(x)={\Omega \over 2 H_0 (1- \Omega)^{3/2}}(sinh(x)-x)
I am trying to calculate the Hubble Radius, R=c/H(t) where H(t)=(da/dt)/a...