Solving Substitution Problem: \int (x2 +2x +1)e^(-ln(x+1)) dx

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SUMMARY

The discussion focuses on solving the integral \(\int (x^2 + 2x + 1)e^{-\ln(x+1)} dx\). The user successfully factors the integrand to \(\int (x+1)(x+1)e^{-\ln(x+1)} du\) and makes the substitution \(u = (x+1)\), resulting in \(\int u^2 e^{-\ln u} du\). The user inquires whether to use integration by parts for the next steps in solving the integral. Additionally, they seek clarification on how to respond to replies within the forum.

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Homework Statement



[tex]\int[/tex] (x2 +2x +1)e^(-ln(x+1)) dx


Homework Equations






The Attempt at a Solution



I started off by factoring the integrand into:

[tex]\int[/tex] (x+1)(x+1)e^(-ln(x+1)) du

Then I tried to make a substitution:

u=(x+1) so du=dx

This left me with this:

[tex]\int[/tex] u2 e^(-lnu) du

So now do I use integration by parts or something? Thanks in advance for the help. And also, if someone responds to my question and I want to respond back, do I just reply to this same thread or PM the person who responded? I ask this because I don't know if I were to reply to this thread if the person will be notified or not. Thanks again.
 
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