• To: mathgroup at smc.vnet.net
• From: "David Bailey" <db at salford-software.com>
• Date: Sat, 29 Apr 2000 22:05:18 -0400 (EDT)
• Organization: University of Salford, Salford, Manchester, UK
• References: <8e3b5h\$kom@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```<zeno at magicnet.net> wrote in message news:8e3b5h\$kom at smc.vnet.net...
> I symbolically integrated the function..(x^2*(x-1))^(1/3) with respect to
> x.
>
> There is in the answer... Hypergeometric2F1[2/3,2/3,5/3,x]
>
> I can do nothing more with that..it just returns it. A Hypergeometric2F1
> with different parameters like Hypergeometric2F1[2,2,5,x] gives an answer.
I
> am using version 3. Is Mathematica unable to compute it?
>
> I can get the Integral with out the Hypergeometric function on the TI-92+,
> (it gives the answer in a different for using Tan, etc.) but I still would
> like to work with the Mathematica answer.
>

Don't blame Mathematica - blame mathematics! Some integrals can be done
analytically, others can't. By using special functions such as the
hypergeometric functions you can increase the number of integrals that can
be solved. The hypergeometric functions depend on a number of parameters in
addition to the main variable. For some values of these parameters the
function can be reduced to an expression involving simpler things such as
trig/exp functions etc. For other values of the parameters no such
simplification is possible. Mathematica can of course compute a value for
Hypergeometric2F1 if you give it a numeric answer - just as it can for Exp
(say).

It would be interesting to know what symbolic answer the TI-92 gave. You
might want to compare the two results for a range of values of x, and also
compare them with a numerical evaluation of the integral - after all the
TI-92 result might be a mistake!

David Bailey
Salford Software

```

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