Resources for learning Elliptic Integrals During a quiz my Calc 3 professor made a typo.  He corrected it in class, but he offered a challenge to anyone who could solve the integral.
The (original) question was:
Find the length of the curve as described by the vector valued function $\vec{r} = \frac{1}{3}t^{3}\vec{i} + t^{2}\vec{j} + 4t\vec{k} $ where $0 \le t \le 3$
This give us:
$\int_0^3 \! \sqrt{t^{4}+4t^{2}+16} \, \mathrm{d}t$
Wolfram Alpha says that the solution to this involves Incomplete Elliptic Integrals of the First and Second Kinds.  I was wondering if anyone had any level appropriate resources where I can find information about how to attack integrals like this.
Thanks in advance.

There are plenty of places to look (for example, most any older 2-semester advanced undergraduate "mathematics for physicists" or "mathematics for engineers" text), but given that you're in Calculus III, some of these might be too advanced. If you can find a copy (your college library may have a copy, or might be able to get a copy using interlibrary loan), I strongly recommend the treatment of elliptic integrals at the end of G. M. Fichtenholz's book The Indefinite Integral (translated to English by Richard A. Silverman in 1971). Also, the books below might be useful, but Fichtenholz's book would be much better suited for you, I think. (I happen to have a copy of Fichtenholz's book and Bowman's book, by the way.)
Arthur Latham Baker, Elliptic functions: An Elementary Text-book for Students of Mathematics (1906) http://books.google.com/books?id=EjYaAAAAYAAJ
Alfred Cardew Dixon, The Elementary Properties of the Elliptic Functions With Examples (1894) http://books.google.com/books?id=Gx4SAAAAYAAJ
Frank Bowman, Introduction to Elliptic Functions With Applications (reprinted by Dover Publications in 1961)
