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Mar 28, 2018 at 19:46 comment added user57225 Can you tell me why some integrals, for instance NIntegral of x^-0.5 from 0 to 1 is converging. Although there is singularity in 0?
Mar 28, 2018 at 18:40 comment added user64494 Yes, the singularity at $x=0$ causes the divergence in view of Series[1/(x - x*Log[x]), {x, 0, 2}] which outputs $$\frac{1}{x (1-\log (x))}+O\left(x^4\right). $$
Mar 28, 2018 at 18:33 history answered Sungmin CC BY-SA 3.0