Arc Length Parameterization

Well here I am again, I'm completely lost on how to do this problem.

it is as followed:

Find an arc length parametrization of r(t) = < t2, t3 >.

The answer is in the form R(s)=< , >

Ive been following my instructions in the book, but this problem is must tricker than the book version.

First i found

$\displaystyle ||r'(t)|| = t sqrt(4+9t) $

I'm being told to then integrate this to find the arc length function, which is bound over the limits of 0->t

$\displaystyle s(t) = 1/27 (4+9t^2)^3/2 + 8 $

changing this function to be g(s) we get this horrific equation of

$\displaystyle sqrt(((27s-8)^2/3)-4)/9) $

then you plug that into the equation up top, and it fails

what do i do?