# Improper Integration Step by Step

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

• Can you get the step-by-step solution in W|A? Oct 15, 2017 at 20:27
• Yes, without any problem actually Oct 16, 2017 at 11:03
• Your query in the OP didn't work for me. I was wondering, What query actually worked? Oct 17, 2017 at 0:30
• Both work in Mathematica and Alpha (for the latter, just introduce the string enclosed by quotation marks) Oct 17, 2017 at 10:18
• 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. Oct 17, 2017 at 12:23

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[ 