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Integral problem

  1. Jan 7, 2012 #1
    1. The problem statement, all variables and given/known data

    2e2gumw.png
    (ignore what's written, it isn't important for the problem)

    I'm studying integrals and I came across this solved example. However I can't understand where the minus of the integral came from came from.

    2. Relevant equations



    3. The attempt at a solution

    The primitive of a f^p * f ' function is f^(p+1) / (p+1) Therefore it should be ln^2(x-1)/2 and not -ln^2(x-1)/2

    Thanks
     
  2. jcsd
  3. Jan 7, 2012 #2
    You could dispel any doubts by making a u-substitution. Try [itex]u = 1 - x[/itex] and see where that takes you.
     
  4. Jan 7, 2012 #3

    SammyS

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    By the chain rule: [itex]\displaystyle \frac{d}{dx}\ln(1-x)=\frac{1}{1-x}\frac{d}{dx}(1-x)=-\frac{1}{1-x}\,.[/itex]

    So you have the anti-derivative of f^p * (- f ' ) .
     
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