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Is the textbook's answer correct?

  1. Nov 25, 2005 #1
    A pretty simple question that is doing my head in is the folllowing:
    Integrate (x+1)/x(2x+1) w.r.t.x
    by choosing to use partial fractions of the form A/x + B/2x+1 my working is as follows:
    using the cover up method and x = 0 to find A I get A =1 ...(0+1)/(2(0)+1)
    using x = -1/2 to find B I get B = -1...((-1/2+1)/-1/2)
    this leaves me with 1/x - 1/(2x+1) to be integrated.
    my answer being lnA + lnx +1/2ln(2x+1) or lnA(x/((2x+1)^(1/2)) (because 1 is half the derivative of 2x)...the books answer is simply ln(x/2x+1)...they omit the constant by specifying that all answers should include it...My question is: is there something wrong with my working or is the book's answer wrong and I should move on?
  2. jcsd
  3. Nov 25, 2005 #2

    Physics Monkey

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    You have the partial fraction decomposition right, and you've integrated correctly (except for a typo). It looks like the book answer is wrong.
  4. Nov 25, 2005 #3
    grrrr nasty textbook! Cheers PhysicsMonkey :smile:
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