Simplifying Integration by Parts: Understanding the Solution

[Jay9313]

Homework Statement

∫ln(2x+1) Integrate by parts

Homework Equations

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

The Attempt at a Solution

The solution is \frac{1}{2}(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?

 

[Villyer]

Look at the first two terms of your answer. Is there a common factor there that you can pull out?

 

[Jay9313]

ln(2x+1) But I don't see how that will help?

 

[Jay9313]

Oh, you can pull the term out, substitute your x from your u substitution, combine some terms, and you get it! Thanks!

 

[Villyer]

Glad I could help :)