For two improper integrals, my textbook claims that ##\displaystyle \int_0^3 \frac{dx}{(x-1)^{2/3}} = 3(1+2^{\frac{1}{3}})## and that ##\displaystyle \int_0^8 \frac{dx}{x-2} = \log 3##. However, when I put these through Wolfram Alpha, the former exists but the latter does not, and it says that the "principle value" is ##\log 3##. I am not sure why there is this discrepancy, but it would be nice if someone could explain(adsbygoogle = window.adsbygoogle || []).push({});

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# I Evaluating improper integrals with singularities

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