# Quantum Mechanics integral for Dirac Delta with abs value

## Homework Statement

Break integral into positive and negative, integrate, recombine and simplify and show that it reduces to a real-valued function. (See attachments)

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## The Attempt at a Solution

My solution is not reducing to a real-valued function. Please see attachments

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You made the substitution $u = i k(x+\alpha-x')$. Note that expansion of this expression gives a term of the form $i k \alpha$. But in the original integral, $k \alpha$ is not multiplied by $i$.