Intergrating a derivative of absolute value in exponential

[myoikos]

hey~ folks!

i'm in trouble with this integral problem.

the range of the integral is from -∞ to ∞ and it has x as independent value.

and the integrand is a derivative of absolute value in exponential;

∫$^{∞}_{-∞}$ (d/dx e$^{-a|x|}$)dx

any idea for the problem??

 

[Hootenanny]

hey~ folks!

i'm in trouble with this integral problem.

the range of the integral is from -∞ to ∞ and it has x as independent value.

and the integrand is a derivative of absolute value in exponential; e$^{a|x|}$

any idea for the problem??

Welcome to Physics Forums.

What is the definition of the absolute value function? Can you think of a way to re-write the integrand without the absolute value sign?

 

[MisterX]

Use a technique like one might use when integrating other piecewise functions; that integral can be expressed as the sum of two definite integrals.

 

[SammyS]

Is the constant, α, positive ?