Infinite integrals of exponential functions

atomicpedals

1. The problem statement, all variables and given/known data

[itex]\int[/itex]|e^-k|x-a||²dx

This integral is from -inf to +inf

2. Relevant equations

A table of integrals would seem to be needed.

3. The attempt at a solution

[itex]\int[/itex]|e^-k|x-a||²dx

=[itex]\int[/itex]|e^-2k|x-a||dx

from here it would seem to simplify down to a variation on the theme of [itex]\int[/itex]|e^-ax|dx where a would be -2k and x would be |x-a| but I'm not sure. Two basic questions come to mind right away: a) am I on the right general track? and b) looking through a standard table of integrals there is plenty on the integral of e^ax but no mention of the integral of e^-ax which leads me to think there's something deeper here that I'm failing to grasp.