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

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Answer 1 · 2018-07-25T17:44:33

see answer below

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#