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First, if you use Integrate, you should define your function exactly. Don't use approximate numbers like 0.99005. f[x_] = -(x/(10^20*(99005/100000 - Exp[x/10^12]))) Integrate[f[x], {x, 0, 10^9}] (* Complicated exact expression involving Log and PolyLog *) Evaluating this approximately indeed yields a small imaginary part. %//N (* 0.471182 - ...

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