Integration bug



This bug is in close connection with another one.. 
Substitution t=cos(u) reduce integral to table form 
defint(t^2/sqrt(1-t^2)/(1+b^2*t^2),t,-1,1) -> 
pi/b^2-defint(1/(1+b^2*cos(t)^2),t,0,pi)/b^2.
Maxima fails on defint(1/(1+b^2*cos(t)^2),t,0,pi) as well

The same problem will be with
defint(t^(2*n)/sqrt(1-t^2)/(1+b^2*t^2)^m,t,-1,1), where n,m=1,2,3..


I find that the maple 
On Tuesday 10 June 2003 19:29, Stavros Macrakis wrote:
>> I'm sorry
>> Integrand is  t^2/sqrt(1-t^2)/(1+b^2*t^2)
>
>Well, defint got the other case wrong, too, so that was useful to
>know....
>
>      -s