about bug 1044318



>>>>> "Valery" == Valery Pipin <pip at iszf.irk.ru> writes:

    Valery> This  bug is marked as solved
    >> * 1044318: defint(1/(sin(x)^2+1),x,0,3*%pi) wrong
    Valery> Indeed defint(1/(sin(x)^2+1),x,0,3*%pi) give the right answer -> 3 sqrt(2) 
    Valery> pi/2.

    Valery> however 
    Valery> defint(1/(a^2*sin(x)^2+1),x,0,3*%pi) still gives 0

Does it?  Here's what I get:

(%i9) integrate(1/(1+a^2*sin(x)^2),x,0,3*%pi);
	       2	      2
Is  a (a sqrt(a  + 1) + sqrt(a ))  positive, negative, or zero?

pos;
	    2	      2
Is  2 sqrt(a  + 1) - a  - 2  positive, negative, or zero?

neg;
			  2	    2
Is  abs(a) - sqrt(2 sqrt(a  + 1) + a  + 2)  positive, negative, or zero?

neg;
			    2	      2
Is  abs(a) - sqrt(- 2 sqrt(a  + 1) + a  + 2)  positive, negative, or zero?

pos;
				    3 %pi
(%o9) 				 ------------
				       2
				 sqrt(a  + 1)

(I answered the questions assuming a = 1).
And for a = 1, we get right answer.

Ray