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Mathematica

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  • $\begingroup$ Please explain the down-vote. What is incorrect in my answer? $\endgroup$ Commented Mar 26, 2022 at 12:36
  • $\begingroup$ –1: your answer is obviously wrong. A simple With[{a = 0.2, b = 0.3, c = 0.4}, LogPlot[1/((-(a - I b) + (x + I c)^2) (-(a + I b) + (x - I c)^2)), {x, -10, 10}]] shows that the integrand is positive-definite and therefore the integral must be positive for these specific values of $a, b, c$ (which I've picked at random). $\endgroup$ Commented Mar 28, 2022 at 8:16
  • $\begingroup$ @Roman: Master your math. The Mathematica answer claims that the integral equals zero under the certain impossible condition. Don't hesitate to ask for further explanation in need. $\endgroup$ Commented Mar 30, 2022 at 5:23
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    $\begingroup$ Technically you are right; in practice, this answer is useless because wrong for all values of $a,b,c$. What the OP wants is an expression that gives the integral in question, and not a counter-factual but "technically correct" mathematical subtlety. "The integral is zero whenever your parameters satisfy a non-satisfiable condition" is not a useful answer; calling it "mathematically correct" does not help in practice. $\endgroup$ Commented Mar 30, 2022 at 8:00
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    $\begingroup$ @Roman has hit the heart of the matter: mathematics as practiced by most of us is useful. Sophistry is useless. $\endgroup$ Commented Mar 30, 2022 at 12:44