Inverse second moment of the chi-square distribution: $\mathbb{E}[(\chi^2_d)^{-2}] = 1/((d-2)(d-4))$ for $d \ge 5$

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Inverse second moment of the chi-square distribution: $\mathbb{E}[(\chi^2_d)^{-2}] = 1/((d-2)(d-4))$ for $d \ge 5$ · Prove2Me