I tried to expand the term in the integral but it turns out to be of order 1/x and diverges... Any help is appreciated! Thanks in advance! $\int_{0}^{\infty}\sqrt{\log (1+1/x^2)}dx<\infty?$
2026-03-27 07:30:44.1774596644
Prove this improper integral is finite
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This expression is good to check the integrability at $\infty$. For the integrability in 0, try to set $1/x^2=t$.