mark mcclure wrote:

> There's a lovely little article in the February 2009 issue
> of the monthly on using integrals to approximate pi.  The
> author "discovers" some nice rational approximations of pi
> by systmeatically searching through integrals of the
> form
>
> integrate(
>     (x^m * (1 - x)^n * (a + b*x + c*x^2))/(1 + x^2),
>   x, 0, 1)
>
> with Maple.  Unfortunately, Maxima (and therefore Sage)
> cannot do these integrals.

Maybe a different example is needed; Maxima can now
compute such integrals. (The code was in CVS at the time
and now it's been released.) Maxima's symbolic integration
has been greatly strengthened by recent work of Dieter Kaiser
and Raymond Toy.

FWIW

Robert Dodier

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