Computing Fourier transforms with exponentials

[js10j2jh]

Homework Statement

Compute the Fourier transform of f(x)=exp(-b|x|), b>0

Homework Equations

F(k)=1/2pi(integral[inf,-inf]f(x)exp(ikx)dx)

The Attempt at a Solution

F(k)=1/2pi(integral[inf,-inf]exp(ikx-b|x|)

How do I solve this? I've tried to solve it but can't get to a solution because of the modulus sign.

 

[sunjin09]

write the integral as sum of two integrals and integrate each one of them.

 

[js10j2jh]

Thank you!