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I am having difficulty solving the following integral:

[tex]

\int^{\infty}_{-\infty}e{-(a|x|+ikx)}dx

[/tex]

I have tried to use an explicit form of the absolute, eg.

[tex]

-(a|x|+ikx) = \left\{\stackrel{-(ik+a)x\ x>0} {-(ik-a)\ x<0}

[/tex]

Does this allow me to seperate the integral into a sum of two integrals?

[tex]

\int^{0}_{-\infty}e{-(ik+a)x}dx+\int^{\infty}_{0}e{-(ik+a)x}dx

[/tex]

This was my best guess, but the result I got did not converge, so either I did the integral improperly, or else this is not a legal method.

Would someone be so kind as to share their knowledge?

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# Integral of exponential absolute functions

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