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I tried the following integration

Integrate[DiracDelta[Tan[x]], {x, -4, 4}]

I got 1 as the result. However, between -4 and 4 Tan[x] has 3 roots. x0=-Pi, x1=0 and x2=+Pi

On paper, I would use the scaling and multiple zeros rules of the dirac delta function which converts the integrand into 3 integrands each of the form DiracDelta[x-x_i] with the scaling function 1/Abs[1+Tan[x_i]^2] infront. Each scaling factor evaluates to 1 at each root, and the integration over the each 3 dirac deltas return 1 which sums up to 3 not 1.

Why does MMA give 1? Could anyone explain the math behind MMA's result?

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    $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – Mr.Wizard
    Commented Jun 21, 2020 at 11:40
  • $\begingroup$ It might just be a bug. That part of the integrate code might have trouble when the part inside is not a linear expression in the variable of interest. (Or maybe it handles some generalizations but not all). $\endgroup$
    – Daniel Lichtblau
    Commented Jun 21, 2020 at 15:16

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