In addition, if you use the version 10 or higher, you can use the new ArcLength command:
ArcLength[{x, x^3 - 9 x}, {x, 0, 3.0}]
for easier input, and works in all dimensions and can also work in different coordinate systems.
I can also not recreate your complex output (version 10.3 on OSX El Capitan).
