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NIntegrate does each integral separately This has been observed before: NIntegrate piecewise vector function, Nested NIntegrate of vector function. It is also clear from the following BenchmarkPlot: int[n_] := Block[{shaxis}, shaxis = Table[1.0*i, {i, 1, n}]; NIntegrate[shaxis/(x^3 + 10), {x, 0, Infinity}, Method -> {"GlobalAdaptive", Method ...

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