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Integration with fraction and square root

  1. Jan 27, 2009 #1
    i am given this function and need to integrate it

    [tex]\frac{4x+7}{\sqrt{-4x^2+20x-9}}[/tex]

    i have been trying to intergrate it by calling something T, preferably the expression under the sqrd root, or part thereof (-4x2+20x=T) but i cant find the way to do this, cant find the best expression that fits both the denominator and numerator of the fraction.. any other ideas??
     
    Last edited: Jan 27, 2009
  2. jcsd
  3. Jan 27, 2009 #2

    Mark44

    Staff: Mentor

    Try u = -4x^2 + 20x - 9, and du = (-8x + 20)dx (I like u for substitutions better than T.)

    Your numerator is 4x + 7 = 4x -10 + 17, so your integral can be rewritten as two integrals.

    [tex]\int \frac{4x - 10}{\sqrt{-4x^2 + 20x - 9}}dx + \int \frac{17}{\sqrt{-4x^2 + 20x - 9}}dx[/tex]

    Applying the substitution in the first integral, we have [itex]-1/2\int du/u^{1/2}[/itex]. The second one is probably amenable to a trig substitution.
     
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