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 Nov20 awarded Popular Question Jul2 awarded Curious Aug3 awarded Yearling Jul9 accepted Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$ Jul9 comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$ Thanks! Everything clear now. Jul9 comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$ This is as a close to an answer as I can get, but before I accept it, one thing to clarify: this measure theory stuff is related to Lebesgue integration and the given integral can be shown, using Lebegue theory, to be convergent and its value is zero. Is that what are you are saying? Jul9 comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$ @DonAntonio No was confused about the comment itself not my question. The comment was somewhat contradictory but N.S. cleared things. Anyway, I've edited the question to be clear about what I'm asking for. Different? Oh well, then I'll post a new question. thx! Jul9 revised Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$ Cleared question Jul9 comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$ @Omnomnomnom Yes you actually understood my question!! Thx. @ ZettaSuro : I assume you we responding to N.S. comment.. Jul9 comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$ @DonAntonio I do know it is not convergent and how to to show, was rather confused about what N.S. meant. My question is more like this: Riemann integration says this integral diverges. Does this mean Lebegue integration and other integration theories will behave the same with this integral? [Should probably put this in question]. Jul9 comment Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$ @N.S. no method can show this integral is convergent,...,since it is not convergent: how do you know it is not convergent if there is no method to show that? I'm a tad confused here. :-( Jul9 asked Evaluate $\int \limits_{0}^{\infty} \frac{x}{1+x^2} dx$ Feb19 comment Verification of a proof involving Hausdorff max. principle and collections @AsafKaragila Thanks for the patience and corrections!!! Feb19 revised Verification of a proof involving Hausdorff max. principle and collections And so S  is monotone. Feb19 revised Verification of a proof involving Hausdorff max. principle and collections Changed notation as not to imply index on sets are indexing sets Feb19 comment Verification of a proof involving Hausdorff max. principle and collections @AsafKaragila The basics are never funny! :-) Thanks very much!!! Feb19 revised Verification of a proof involving Hausdorff max. principle and collections deleted 90 characters in body Feb19 accepted Verification of a proof involving Hausdorff max. principle and collections Feb19 revised Verification of a proof involving Hausdorff max. principle and collections deleted 4 characters in body Feb19 revised Verification of a proof involving Hausdorff max. principle and collections added 4 characters in body