Bug 754823 integrate(x^2/sqrt(1-x^2)/(1+x^2))

>>>>> "Richard" == Richard Fateman <fateman at cs.berkeley.edu> writes:


    >> G&R gives some methods for integrating functions of the form
    >> 1/(e+f*x+g*x^2)/sqrt(a+b*x+c*x^2), but I'm too lazy to
    >> implement them right now.
    >> 
    >> 
    Richard> Here is the formula from Mathematica.

[snip]

Thanks for the result.  If someone ever gets around to enhancing
maxima, this is a useful result to compare against.

    >> So, for now, I'm going to modify maxima so that this integral and
    >> similar integrals will return the integral.
    >> 
    >> How does that sound?
    >> 
    Richard> If it avoids giving a definitely wrong answer, sure.

My thoughts exactly.

But I have to say, I'm not 100% sure the answer is wrong because
maxima does some things that makes it hard to compare.  radcan
converts sqrt(1-x) to %i*sqrt(x-1) in some cases (even when radexpand
is false) and then it can't simplify it further.  And the expressions
are messy enough that I don't want to verify them by hand.  I suppose
I could use some numerical evaluations to test....

Ray