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Integration By Parts: Need help with a step

  1. Aug 2, 2009 #1
    Integration By Parts: Need help with a step....

    Evaluate the integral:

    [tex]\int[/tex] ln(2x + 1)dx

    I worked it out up until:

    Xln(2x + 1) - [tex]\int[/tex] 2x/(2x + 1) dx

    Then the next step throws me off. I attached a scan from the solutions manual and circled the part that confused me. Could somebody explain how we went from "2x/(2x + 1)" to "[(2x + 1) - 1]/(2x + 1)"?

    I'm sure it's a simple arithmetic step I'm overlooking, which is why I'm reviewing a few weeks before Calc. 2.


    e8Pdk.jpg
     
  2. jcsd
  3. Aug 2, 2009 #2

    Cyosis

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    Re: Integration By Parts: Need help with a step....

    Not much happens really, [itex](2x+1)-1=2x+1-1=2x[/itex]. As you can see both numerators are the same, the latter is just written in a more useful form.
     
  4. Aug 2, 2009 #3
    Re: Integration By Parts: Need help with a step....

    thanks.... it makes sense now...
     
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