Is there a way to preform this integral such that the answer is $e^{-|y|}$?

Consider the function $f(y)=e^{-|y|}e^{y}$

I am trying to integrate this function with respect to another variable (such as $x$) so that the result from the integration is $e^{-|y|}$?

The function $f(y)$ can be changed in anyway as long as

1) the powers of $y$ and $|y|$ stay equal to one.

2) and the boundaries of integration do not include $y$ in them.

3) The result of the integral is $e^{-|y|}$. Of course the answer may be of the form $A e^{-a|y+b|}$ where $A$, $a$ and $b$ are constants.

So for example we can add a constant or $x$ inside the $||$ or multiply $y$.

So for example the integral

$$\int^{c_2}_{c1}e^{-|x y+a|}e^{y/x}dx$$

or

$$\int^{c_2}_{c1}(e^{-|ay+x|}e^{y+b}+d)dx$$

Is there a way to integrate this so that the answer is $e^{-|y|}$?

We are free to choose where to put the constants or $x$ as long as the three conditions are satisfied.

from Hot Weekly Questions - Mathematics Stack Exchange