In 12.0.0 for Microsoft Windows (64-bit) (April 6, 2019) writing:

Integrate[D[ArcTan[Sqrt[1 + x^5]], x], x]

I get:

ArcTan[Sqrt[1 + x^5]]

but if I write:

Integrate[D[ArcTan[x Sqrt[1 + x^5]], x], x]

Mathematica can no longer solve the integral. Does anything escape me?

  • 1
    $\begingroup$ Interesting. But it can do D[Integrate[ArcTan[x Sqrt[1 + x^5]], x], x]. $\endgroup$ – Bill Watts Jul 5 at 17:41
  • $\begingroup$ Mysteries of the CAS! In my opinion, this is the current limit of the CAS of Mathematica compared to Rubi that is not deceived in these integrals. $\endgroup$ – TeM Jul 5 at 17:43
  • 2
    $\begingroup$ Trace@D[Integrate[ArcTan[x Sqrt[1 + x^5]], x], x] makes obvious why this way is easier... $\endgroup$ – Michael E2 Jul 5 at 17:56

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