Question

Fourier Transform of a space, f(k)
f(x)=e^(-a*abs(x))

Answer 1

So far I have split the integrals into two pieces.
Intg[e^x(a+ik),-inf,0] + Intg[e^x(-a+ik),0,inf]

Answer 2

I already know the answer, (sqrt(2/pi)*a/a^2+k^2). I don't understand where the sqrt(2/pi) came from... I know that's the result of integrating a gaussian.. However, getting to that is the difficult part.

Answer 3

Also, a>0.