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I have difficulty in figuring out the following integral:

[itex] I(l,m;z) = \int^1_0 dx~\frac{x^l}{z - x^m} [/itex],

where [itex] l [/itex] and [itex] m [/itex] are integers, while [itex] z = \omega + i0_+[/itex] is a complex number that is infinitely close to the real axis. What is interesting to me is when [itex] \omega [/itex] is close to zero, so that the integrand bears a singularity in the domain.

Could somebody help me out ?

Thanks a lot !

hiyok

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# How to do this integral ?

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