How do you integrate $f(x) = e^-|13x|$ ?

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Answer 1 · 2018-07-25T17:44:33

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Given function:

$f(x)=e^{-|13x|}$

1) If $x<0$ $\implies f(x)=e^{13x}$

$\int f(x)\ dx$

$=\int e^{13x}\ dx=1/13e^{13x}+C$

1) If $x ge 0$ $\implies f(x)=e^{-13x}$

$\int f(x)\ dx$

$=\int e^{-13x}\ dx=-1/13e^{-13x}+C$

How do you integrate f(x) = e^-|13x|f(x) = e^-|13x|?