Your are talking about reduction to elliptic integrals -

https://en.wikipedia.org/wiki/Elliptic_integral

I do not think that sympy can currently do this (it would be a great
project)!


On Mon, Feb 15, 2016 at 10:01 AM, Andrew Corrigan <[email protected]
> wrote:

> Thank you both for your replies.  I'm not sure I follow the discussion to
> be honest as to how it applies to my original problem.  In particular:
>
>> Distilling this down you want to compute the integral of the square
>>> root of a quadratic
>>
>> I'm not sure that is accurate.  If you are just referring to that it is
> (foo(xi))**2  + (bar(xi))**2, then yes the expression is quadratic in foo
> and bar.  But in general, foo(xi) and bar(xi) are themselves higher degree
> polynomials of xi (and in higher dimensions other coordinates too).  This
> is a very simple and minimal reproducing example: in this case foo and bar
> are linear polynomials so the whole expression is quadratic.  I have
> expressions I need to integrate, where foo(xi) and bar(xi) are higher-order
> polynomials terms of xi.
>
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