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## Main Question or Discussion Point

Recently I fruitlessly asked if anybody could help with the definite integral of

sin(a x) / ( x sqrt(-(x-q1)(x-q2)) )

from x=q1 to x=q2 where a,x, q1 and q2 are all real.

If the sqrt wasn't there one could use contour integration and consider residues at q1,q2 and 0 but with the sqrt I am somewhat stumped.

Yet this seems an obvious area to me: integrations between the roots of a quadratic Q(x) of functions of the form f(x) / Q(x)^alpha .

Is this really virgin territory?

sin(a x) / ( x sqrt(-(x-q1)(x-q2)) )

from x=q1 to x=q2 where a,x, q1 and q2 are all real.

If the sqrt wasn't there one could use contour integration and consider residues at q1,q2 and 0 but with the sqrt I am somewhat stumped.

Yet this seems an obvious area to me: integrations between the roots of a quadratic Q(x) of functions of the form f(x) / Q(x)^alpha .

Is this really virgin territory?