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Homework Statement
[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.