(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int x* exp(-\alpha x -ikx)dx[/tex]

the integration is definite with limits (x: 0---->inf)

alpha , k are real constants

2. The attempt at a solution

I used integration by parts and arrived at the result

[tex]\frac{xexp(-\alpha x-ikx)}{\alpha+ik}[/tex] + [tex]\frac{exp(-\alpha x-ikx)}{(\alpha+ik)^{2}}[/tex]

now when i come to substitute by the integration limits comes the problem. How to deal with inf. ??

I know that the complex exponential functions are periodic , so there limit when x-->inf will never have certain value.

Any suggetions will be highly appreicated.

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# Homework Help: Integration involving complex numbers

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