Simplifying Integration by Parts: Understanding the Solution

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Homework Help Overview

The discussion revolves around the integration of the function ln(2x+1) using integration by parts. Participants are examining the relationship between two different expressions that represent the same integral result.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand why their initial answer differs from another expression that is claimed to be equivalent. Participants explore the possibility of simplifying the original answer by factoring and substituting terms.

Discussion Status

Some participants have offered guidance on factoring and combining terms, suggesting a productive direction in clarifying the relationship between the two expressions. However, there is no explicit consensus on the simplification process itself.

Contextual Notes

The original poster expresses frustration over the inability to simplify their answer to match another form, indicating a potential gap in understanding the algebraic manipulation involved.

Jay9313
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Homework Statement



∫ln(2x+1) Integrate by parts

Homework Equations



I got xln(2x+1)+[itex]\frac{1}2{}[/itex]ln(2x+1)-x+C

The Attempt at a Solution



The solution is [itex]\frac{1}{2}[/itex](2x+1)ln(2x+1)-x+C

I know the answers are the same,but it's bugging me that I can't simplify the first answer I got to the second answer. Can someone explain it to me?
 
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Look at the first two terms of your answer. Is there a common factor there that you can pull out?
 
ln(2x+1) But I don't see how that will help?
 
Oh, you can pull the term out, substitute your x from your u substitution, combine some terms, and you get it! Thanks!
 
Glad I could help :)
 

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