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## Homework Statement

Prove that the convolution of [itex]e^{-\left|x\right|}[/itex] is [itex](1-x)e^{x}[/itex] for x<0 and [itex](1+x)e^{-x}[/itex] for x>0

## Homework Equations

## The Attempt at a Solution

I plug through the integral in the standard way and take the limits as x tends to positive and negative infinity etc. But, I keep getting that the convolution is zero?

Any help would be greatly appreciated.