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Math Help - Contour integration

  1. #1
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    Contour integration

    I am trying to solve \int^{+\infty}_{-\infty}\frac{1}{x}dx I read that it is a contour integral along the semi-circle of large radius in the lower complex plane, firstly is there any justification for this and secodnly does the integral then become  \int^{\pi}_{0} i d\theta
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  2. #2
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    Re: Contour integration

    I expect you have to use the parameterisation \displaystyle x = r\,e^{i\theta} \implies dx = i\,r\,e^{i\theta}\,d\theta .
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