Indefinite integral for the square root of a quartic function

[StTheo]

I arrived at this problem while trying to find the length of a 3D http://en.wikipedia.org/wiki/Cubic_interpolation" [Broken].

Basically, I'm having to figure out how to integrate ((At⁴+Bt³+Ct²+Dt+E)^1/2)dt

A,B,C,D, and E are constants which have to be plugged in after integration, I'm sorry to say.

All the reduction formulas I've seen use quadratic functions of some kind, so would I have to convert the quartic function into some kind of quadratic function?

 

[Char. Limit]

In general, it cannot be done simply, I believe. From what I can tell using Wolfram-Alpha, the integral involves the inverse sine function as well as the elliptic integrals of the first AND third kinds. It can't evaluate the integral, though: here.

 

[StTheo]

Grr, oh well. However, I hadn't seen that wonderful site you linked to before. I'll probably waste quite a bit of time on it.