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Using U-Substitution to Find an Integral

  1. Jun 22, 2013 #1
    So I was messing around with some basic u-sub calculus and came across this problem. Any help would be greatly appreciated!

    1. The problem statement, all variables and given/known data

    [itex]\int[/itex] [itex]\frac{3x^{2}}{x^{2}-7}[/itex] dx

    2. Relevant equations
    I'm using u-substitution, as stated at the beginning.

    3. The attempt at a solution
    I see that the u could be the denominator and the numerator is the derivative, or du.

    [itex]\int[/itex] [itex]\frac{du}{u}[/itex]

    [itex]\int[/itex] [itex]\frac{1}{u}[/itex] du

    ln|u|+C

    ln|x[itex]^{2}[/itex]|+C

    I'm pretty sure this is the correct answer, but I decided to integrate it with the boundaries x=1 and x=4.5.

    [ln|x[itex]^{2}[/itex]-7|][itex]^{4.5}_{1}[/itex]

    ln|13.25| - ln|-6|
    ln(13.25) - ln(6)
    2.5839-1.7917
    .7922

    So this is my final answer, but it just doesn't seem right. I graphed the function and saw it was under the x-axis. Is this the problem?
     
  2. jcsd
  3. Jun 22, 2013 #2

    LCKurtz

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    But if ##u=x^2-7## then ##du = 2xdx## and that is not what you have in the numerator. Try one long division step and see what to do next.
     
  4. Jun 22, 2013 #3

    Zondrina

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    Following what Lc suggested, here's a hint that will make it easier : ##x^2 - 7 = (x + \sqrt{7})(x - \sqrt{7})##.
     
  5. Jun 23, 2013 #4
    Oh man I feel like an idiot!! Thankyou all!
     
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