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I am trying to obtain the step-by-step analysis of the integral $\int _{ 0 }^{ \infty }{ { y }^{ 3 }{ e }^{ -\frac { y }{ N } }dy }$ by calling Wolfram Alpha:

WolframAlpha["integrate ((y^3)*exp(-y/N)) from 0 to Infinity", 
 PodStates -> {"Input__Step-by-step solution"}]

However, I only get the option to see the step-by-step solution for the indefinite case:

enter image description here

Simply changing the integration limits, avoiding infinity, allows me to see the whole process:

WolframAlpha["integrate ((y^3)*exp(-y/N)) from 0 to 9999", 
 PodStates -> {"Input__Step-by-step solution"}]

enter image description here

Why does this happen? How can I see the whole step-by-step solution of this improper integral?

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  • $\begingroup$ Can you get the step-by-step solution in W|A? $\endgroup$
    – Goofy
    Commented Oct 15, 2017 at 20:27
  • $\begingroup$ Yes, without any problem actually $\endgroup$
    – jlnkls
    Commented Oct 16, 2017 at 11:03
  • $\begingroup$ Your query in the OP didn't work for me. I was wondering, What query actually worked? $\endgroup$
    – Goofy
    Commented Oct 17, 2017 at 0:30
  • $\begingroup$ Both work in Mathematica and Alpha (for the latter, just introduce the string enclosed by quotation marks) $\endgroup$
    – jlnkls
    Commented Oct 17, 2017 at 10:18
  • $\begingroup$ I meant by "work" that it produced the answer you're asking for, that is, the step-by-step solution. Seems unlikely that it works: If it works for you in Mathematica, then why did you ask how to make it work in Mathematica? I thought if you shared what worked in W|A, then someone might be able to make it work in M. -- Seems Chip's partial answer might make the point moot, though. $\endgroup$
    – Goofy
    Commented Oct 17, 2017 at 12:23

1 Answer 1

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The generated condition Re[N] > 0 is tripping things up. A workaround for the time being is to substitute a concrete value for N and substitute back after the fact.

WolframAlpha[
  "integrate ((y^3)*exp(-y/pi)) from 0 to Infinity",
  {{"Input", 2}, "Content"}, 
  PodStates -> {"Input__Step-by-step solution"}
] /. "\[Pi]" -> "N"

enter image description here

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