Friday, December 25, 2015

Improper integration involving complex analytic arguments



I am trying to evaluate the following:




011+xadx, where a>1 and aR



Any help will be much appreciated.


Answer



Use the change of variables 1+xα=1t to cast the integral in terms of the beta function



1α10t1/α(1t)1/α1=1αΓ(1α)Γ(11α)


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