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Integral of type 'derivative over function' with a twist

  1. Nov 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the integral

    [(2x - 3) / (x^2 - 3x - 5)^2] dx

    2. Relevant equations

    I noticed that if I differentiate the denominator I get the nominator, which would be a simple problem. The denominator, however is raised to the power 2.

    Can I still somehow use the rule for integrals where the nominator is the derivative of the denominator? Or do I need to take a different approach?

    Thank you
  2. jcsd
  3. Nov 26, 2009 #2


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    The 'approach' you are talking about is integration by substitution, I hope. You've observed that if u=x^2-3x-5, then du=u'dx=(2x-3)dx. That's great. That turns the integral into du/u^2 in terms of u. Can you integrate that?
  4. Nov 26, 2009 #3
    I got it, thanks an awful lot!
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