In trying to solve [itex]\int^{\infty}_{-\infty} x + \frac{1}{x} dx[/itex] could it be split up and solved using the Cauchy Principle Value theorem and a contour integral along a semi-circle. Thus;(adsbygoogle = window.adsbygoogle || []).push({});

[itex]PV\int^{\infty}_{-\infty}x dx =0 [/itex] [itex]+\int \frac{1}{x} dx = \int^{\pi}_{0} i d\theta [/itex]

Is this valid reasoning?

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# Contour integrals

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