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wondering if it's not analytical, are there any bounds that are possible? Appreciate it if any solutions or comments.

Alexis
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OneCitizen
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    After going back and forth with my (now deleted) comments, I believe the expectation does not exist at all... – B.Liu Mar 02 '22 at 17:55
  • Now I see it. Thanks! – OneCitizen Mar 02 '22 at 18:06
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    @B.Liu That is correct, as shown at https://stats.stackexchange.com/questions/299722. To apply the results, simply notice that $(1+X)^2$ is non-central chi-squared random variable with 1 df. Because its density grows arbitrarily high near $0,$ its reciprocal has an infinite expectation. – whuber Mar 02 '22 at 19:39

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