Integrate[r^2 Sqrt[1 - r^2] Sin[θ]^2 Sin[ξ] Cos[ξ] (r Sin[θ]), {r, 0, 1}, {θ, 0, Pi}, {ξ, 0, Pi/2}]Integrate[r^2 Sqrt[1 - r^2] Sin[θ]^2 Sin[ξ] Cos[ξ] (r Sin[θ]), {r, 0, 1}, {θ, 0, Pi}, {ξ, 0, Pi/2}]

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