I think it was Gauss who calculated a limit in two different ways, getting -1/2 one way and infinity the other. As he didn't see the error, he wrote sarcastically, "-1/2 = infinity. Great is the glory of God" (In Latin). Anyway, it appears that Wolfram Alpha could do the same thing, as I asked it to calculate the integral of x/(x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}-1) dx from x=0 to 2, which it said diverged... presumably having found the limit of the integral from 0 to 1, then from 1 to 2, and concluding that it diverged as soon as an infinity appeared. However, asking it (Wolfram α) to calculate the integral of 1/2*integral of ln |u| du from u = -1 to 3, it comes up with (ln(27)-4)/2, i.e., a finite result, presumably having subtracted the two identical limits before evaluating them. (I don't have "Pro" so I can only guess what path it took.) The two results should be equal, (integration by substitution). I am inclined to accept the finite result, but is there something I am missing here? Thanks in advance.

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# Improper integral done two different ways

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