Ok, the problem is there are two curves and I need to find out which is shorter. I can't find the first one so I'll just post that. The other should be easy after I learn how to get this one.
The first curve is:
The Attempt at a Solution
I used the formula and worked it down to .
I've also seen some similar problems to this where people recommended trig substitutions. I tried substituting tan u in which gave me sec^2 u under the radical. If I go that route, I don't know the integral of sec or how you could carry on. The other way I thought you could do this was to just simplify (from the last picture I posted) and try to integrate that... but that would be rough. Any tips?