To verify the improper integral $\int_{1}^{\infty}x\cdot\left | \sin (x^4)\cdot\sin x \right |dx$ converges or diverges,I code

Integrate[x*Abs[Sin[x^4]*Sin[x]], {x, 1, Infinity}]

then feedback is the expression of $\int_{1}^{\infty}x\cdot\left | \sin (x^4)\cdot\sin x \right |dx$.Is that means the improper integral $\int_{1}^{\infty}x\cdot\left | \sin (x^4)\cdot\sin x \right |dx$ converges?

  • $\begingroup$ Obviously, the integral diverges. But it is surprising that the system does not give a message, and estimates the numerical value as 1.5408*10^147 $\endgroup$ – Alex Trounev Jul 3 '19 at 15:33
  • $\begingroup$ @AlexTrounev: Yes,I proved it diverges in the past .But after using mathematica to verify my conclusion, I puzzled ! Thanks for your confirmation ! What's worng with it? $\endgroup$ – AplehKevin Jul 3 '19 at 15:43
  • $\begingroup$ Not all cases have been studied and not all are entered into the database. $\endgroup$ – Alex Trounev Jul 3 '19 at 16:27
  • $\begingroup$ @AlexTrounev:Is there any better way to deal with this kind of problem? $\endgroup$ – AplehKevin Jul 3 '19 at 16:36
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    $\begingroup$ This is rather a math question than a Mathematica question: see math.stackexchange.com/questions/1018348/… . $\endgroup$ – user64494 Jul 4 '19 at 17:04

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