Question

integral from -inf to inf of e^(-|x|)

Any ideas on what I should do?

Answer 1

please, you have to break the integration domain as below:
\[\left( { - \infty ,0} \right) \cup \left( {0, + \infty } \right)\]

Answer 2

you should get this:
\[\int\limits_{ - \infty }^0 {{e^x}} dx + \int\limits_0^{ + \infty } {{e^{ - x}}} dx\]

Answer 3

\[
\Large e^{-|x|} =
\begin{cases}
e^{x} \ \ \ \ \text{if } x < 0 \\
e^{-x} \ \ \text{if } x \ge 0 \\
\end{cases}
\]

as Michele_Laino wrote in his second post

Answer 4

You should also visually try to picture what the function \(e^x\) looks like. that helps too.