Does the Integral of exp((ix-s)*k)/k from 0 to Infinity Converge?

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SUMMARY

The integral of exp((ix-s)*k)/k from 0 to infinity does not converge, as confirmed by Wolfram Alpha. This conclusion is based on the behavior of the integrand as k approaches infinity, where the oscillatory nature of the exponential function combined with the division by k leads to divergence. The discussion emphasizes the importance of understanding the conditions under which integrals converge or diverge in complex analysis.

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form zero to infinity of ((exp((ix-s)*k))/k) dk
 
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