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

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Homework Statement



\int (x2 +2x +1)e^(-ln(x+1)) dx


Homework Equations






The Attempt at a Solution



I started off by factoring the integrand into:

\int (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:

\int 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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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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