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Homework Help: Integrals using log rule

  1. May 6, 2010 #1
    1. The problem statement, all variables and given/known data
    integral of x/square root of 9- x^2

    2. Relevant equations

    1/x dx= ln |x| + c

    3. The attempt at a solution
    3 ln|x| + c
  2. jcsd
  3. May 6, 2010 #2


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    Staff Emeritus
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    You need to show more work. At this point, it looks like you're just guessing.

    So you have the integral

    [tex]I=\int \frac{x}{\sqrt{9-x^2}}\,dx[/tex]

    right? I don't see how

    [tex]\int \frac{dx}{x} = \ln |x| + c[/tex]

    applies at all.
  4. May 6, 2010 #3
    Try factoring out a 9 in the denominator in the square root. It should be somewhat obvious from there what you need to do.
  5. May 6, 2010 #4


    Staff: Mentor

    A simpler approach is to use an ordinary substitution. Using this approach you don't need to factor anything out of the radical.
  6. May 6, 2010 #5
    Oh whoops, I didn't see the x in the numerator. I thought there was only a 1 in the numerator, which is why I thought that at first. You're right.
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