# Need analytic solution!

by quasar_4
Tags: analytic, solution
 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 $$\int$$ exp(-a*abs(x))*exp(i*(k0-k)*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?
 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 $$\frac{1}{a-bi} + \frac{1}{a+bi} = \frac{2a}{a^2+b^2}$$ BTW. $$b = k_0 - k$$ in my solution.