Mathematica [Mathematica] Bug in Integrate with derivatives of a delta function

AI Thread Summary
The discussion highlights a bug in Mathematica 8 related to the integration of expressions involving the derivative of the Dirac delta function. Two integrals, despite being mathematically equivalent, yield results that differ by a sign when evaluated with specific expressions. The issue appears to be linked to how the arguments of the Dirac delta function are structured, particularly with negative powers of x. Users are encouraged to replicate the results, noting that modifying the expressions resolves the discrepancy. This indicates a potential limitation in Mathematica's handling of such integrals under certain conditions.
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Code:
Integrate[f[qs] DiracDelta'[qs (1 - 1/x)], {qs, -\[Infinity], \[Infinity]}, 
 Assumptions -> 0 < x < 1]
Integrate[f[qs] DiracDelta'[qs - qs/x], {qs, -\[Infinity], \[Infinity]}, 
 Assumptions -> 0 < x < 1]

This is on Mathematica 8 for windows.
The results differ by a sign. They are effective the exact same thing, but due to how I write the insides of the dirac delta I get a different result.

Can anyone replicate this?
 
Last edited:
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I notice it is only for the first negative power of x. If you put

[qs (1 - 1/x^(1.))]

[qs - qs/x^(1.)]

it works?
 

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