Hello All! I'm working on educational project and I need to calculate the length of a Bezier curve. I have a cubic Bezier curve given in explicit form.

(1 - k)^3 x0 + 3 (1 - k)^2 k x1 + 3 (1 - k) k^2 x2 + k^3 x3
(1 - k)^3 y0 + 3 (1 - k)^2 k y1 + 3 (1 - k) k^2 y2 + k^3 y3
(1 - k)^3 z0 + 3 (1 - k)^2 k z1 + 3 (1 - k) k^2 z2 + k^3 z3

Ant I'm trying to calculate the symbolic expression of Length using:

intExpr = Sqrt[D[ptx, k]^2 + D[pty, k]^2 + D[ptz, k]^2]

and then

resultExp = Integrate[intExpr, k]

And I get no solution (Mathematica 8.0 used). What I am getting seems to give wrong results even when trying:

serexpr = Series[intExpr , {k, 0, 2}]
resfunc = Integrate[serexpr, {k, 0, 1}]

I wonder to know it is possible in general? Can someone give me any tips with this?

P.S.: Of course i have computations of Length implemented procedurally. The computation calculates sum of segments of curve. But i want to know if it is possible to make Length symbolically?