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Need analytic solution! 
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#1
Apr1708, 10:15 PM

P: 290

Hi everyone. Maple and I have collectively racked our brains and I've tried most of the integration techniques I know. Does anyone know the solution to the integral
[tex]\int[/tex] exp(a*abs(x))*exp(i*(k0k)*x)*dx from infinity to infinity (not sure how to get the limits over the integral sign here in this text box)??? There might be a good change of variables, but my brain is now too fried to think of it. Or does this baby just not have a nice solution? anyone? 


#2
Apr1708, 11:07 PM

P: 84

Not me :O)



#3
Apr1708, 11:13 PM

Sci Advisor
P: 2,751

What? That's trivial if you just split the integral into two parts, one part from infinity to zero and the other from 0 to infinity as it lets you get rid of the annoying abs(x).
I got [tex] \frac{1}{abi} + \frac{1}{a+bi} = \frac{2a}{a^2+b^2}[/tex] BTW. [tex]b = k_0  k[/tex] in my solution. 


#4
Apr1808, 09:02 AM

P: 290

Need analytic solution!
Haha, yes, I realized that once I got home and felt REALLY dumb for posting the previous msg. I think in fact you can use trig identities and Euler's relation as well to split into a sin and cos part, then the sin drops out (since it's over a symmetric interval) and you can take twice the integral of the cos part from 0infinity. That hadn't worked at the time, but it turns out I was being braindead and forgetting to drop my abs. Duh!! That's what I get for doing homework on 2 hours of sleep...



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