Can some one explain why I am getting this wrong

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Homework Help Overview

The discussion revolves around evaluating the integral of the natural logarithm function, specifically the integral of ln(x+x²). Participants are exploring the steps taken in the integration process and the discrepancies between their results and those found in a textbook.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • The original poster describes using integration by parts and substitution in their attempt to solve the integral, but they express confusion over an additional term in their result compared to the textbook. Other participants question the necessity of integration by parts and suggest alternative methods, such as long division.

Discussion Status

The discussion has seen some participants providing insights into the problem-solving process, with one participant indicating they resolved their confusion. However, there remains a lack of consensus on the best approach to the problem, as different methods are being considered.

Contextual Notes

Participants are referencing a specific textbook, Thomas Calculus, and discussing potential errors in substitution methods. There is an indication of previous discussions on the same problem, suggesting it may be a common point of confusion.

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Can some one explain why I am getting this wrong[SOLVED]

Homework Statement


Evaluate
[tex]\int ln(x+x^{2}) dx[/tex]

Homework Equations





The Attempt at a Solution


I integrated by parts to get down to [tex]xln(x+x^{2})-\int \frac{(2x-1)}{x+1}[/tex] I set [tex]u=1+x[/tex] which led to [tex]du=1 dx[/tex] and [tex]x=u-1[/tex] after so evaluation I got down to [tex]-(\int 2 du -\int \frac{1}{u} du)[/tex] and after more substitution and evaluation I got down to [tex]xln(x+x^{2})+ln\left|1+x \right|-2-2x +C[/tex], but my book says that I should have only got -2x and not that extra -2
 
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Nevermind I figured it out
 
Huh weird, this same problem was solved yesterday. Which book are you using for calculus if you don't mind me asking?
 
Thomas Calculus, I still don't get how I messed up on substitution but I just long divided and got the answer
 
You didn't need to use integration by parts though.
 

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