# Integration by Parts evaluation help

1. Apr 7, 2010

### 01010011

Hi,
Can you tell me if I am on the right track with this problem. Thanks in advance.

1. The problem statement, all variables and given/known data
Evaluate the integral using integration by parts

2. Relevant equations
ln(2x + 1)dx

3. The attempt at a solution
ln(2x + 1)dx

= ln(2x + 1) * 1dx

Let U = ln(2x + 1)

therefore du = 1/(2x+1)

dv = 1dx

therefore v = x

Using the formula: $$\int udv = uv - \int vdu$$

= \int ln(2x + 1) * 1dx = ln (2x + 1)(x) - \int (x)(1/2x + 1)

If any of this is correct, I am now stuck at this point.

2. Apr 7, 2010

### gabbagabbahey

Double check that differentiation

Other than that, it looks good so far. As a hint on how to continue, [itex]\frac{2x}{2x+1}=1-\frac{1}{2x+1}[/tex]