clinton bowen wrote:

> I tried some Cosine Transforms found in the book 'Handbook of Integral
> Equations' by  Andrei D. Polyanin and
> Alexander V. Manzhirov into sage and I found that sage was not able to
> perform these integrals.

For the record, what are some of integrals you tried?

> I guess my questions are:
> How powerful is the integrate() function or how well versed is the
> integrate() in sage?
> What is being done to improve the integrate() ?
> Is there something that I could do to help this coming summer to
> improve it?

At present Sage punts to Maxima to compute integrals.
If I am not mistaken the version of Maxima which is bundled
with Sage is a little out of date. I don;t know if the plan is to
continue calling Maxima or to compute integrals in some other way.

Maxima uses several methods to compute integrals.
Definite integrals are, for the most part, handled separately
from indefinite. There is an implementation of the Risch method.
There has been a lot of terrific work lately (thanks to Dieter Kaiser
and Raymond Toy) on integrals of special functions (gamma
function and so on). If you would like to join the fun, I suggest
that you post a message to the Maxima mailing list about it.
See: http://maxima.sourceforge.net/maximalist.html
We would be glad to have your help.

Robert Dodier
Maxima developer

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