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In 11.3.0 for Microsoft Windows (64-bit) (March 7, 2018) writing:

Integrate[D[x*Sqrt[f[x]], x], x]

I would expect:

x*Sqrt[f[x]]

instead MMA fails to integrate.

Do I miss something?

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    $\begingroup$ Integrate internal code simply fails to recognize that the integrand is an exact derivative. $\endgroup$ – Daniel Lichtblau Jan 10 at 22:36
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    $\begingroup$ I think it comes down to simply evaluation order. Mathematica evaluates the derivative first then looks at the result. It does not have a build-in rule for Integrate[D[f[x],x],x]-> f[x]. I do not how to tell Mathematica not to evaluate the derivative first before trying to integrate the result. I tried this in Maple, and Maple seems to have such a rule build it. Screen shot: !Mathematica graphics btw, here is related question integrate-full-derivative $\endgroup$ – Nasser Jan 10 at 22:59
  • $\begingroup$ Ok, I think I understand, thank you very much! $\endgroup$ – TeM Jan 10 at 23:11

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