In my answer book, I noticed that one of the steps were this:
How did the first step lead to the second step? Can someone help me explain how?
$\displaystyle x\ln(2x+1) + \frac{1}{2}\ln(2x+1) =$
factor out $\displaystyle \ln(2x+1)$ ...
$\displaystyle \ln(2x+1) \cdot \left(x + \frac{1}{2}\right) =$
change the appearance of $\displaystyle \left(x + \frac{1}{2}\right)$
$\displaystyle \ln(2x+1) \cdot \frac{1}{2}(2x+1)$