Application of the appropriate member of Table 5.4.1 leads to
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The antiderivative of cannot be found in terms of elementary functions. It is expressed in terms of , the incomplete elliptic integral, and , the complete elliptic integral. The point here is not to have the reader delve into the definitions of these special functions, but rather, to have the reader understand that arc-length integrals are amongst the most difficult integrals to be encountered in a calculus course. If the power of Maple is not to be used to evaluate these integrals, then very few such integrals can be evaluated with just the limited tools of hand-calculations.
