I want to compute the following definite integral, where $z\in(0,1)$: $$ \int_{-1}^{1} dx \int_{-1}^{1} dy \ \frac{z^2 \sqrt{1-x^2} \sqrt{1-y^2} \sqrt{z+\frac{1}{z}-2 x} \sqrt{z+\frac{1}{z}-2 y}}{\pi ^2 \left(z^2-z (x+y)-z (1-x y)+1\right)^2 \left(z^2-z (x+y)+z (1-x y)+1\right)^2} $$ I computed the integral in x and the result is a complicated combination of elliptic integrals, which cannot be integrated further in y as far as I can tell. I was wondering if there is a simpler way to do it. Any suggestion would be much appreciated!
2026-03-28 02:02:27.1774663347
Definite integral with square roots
115 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
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