I would like to find the result for the following integral $$ \int_{-\infty}^\infty x e^{-|x|/a}\cdot e^{-|x-y|/b} \, dx $$
where $a$ and $b$ are constants. $x$ and $y$ are variables
2026-04-04 02:17:21.1775269041
what is the result for the following Integral?
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Hint: break it up into cases depending on the signs of $x$ and $x-y$.