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Basic Integration Techniques

  1. Mar 14, 2013 #1
    1. The problem statement, all variables and given/known data
    I am reviewing some basic integration techniques. how would i evaluate this?

    2. Relevant equations
    [itex]\displaystyle\int {\frac{1}{\sqrt{8x-x^2}} dx}[/itex]

    3. The attempt at a solution
    i've tried multiplying by

    [itex]\frac{\sqrt{8x-x^2}}{\sqrt{8x-x^2}}[/itex] but that isn't getting me anywhere.

    should i use something like completing the square?
  2. jcsd
  3. Mar 14, 2013 #2


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    Staff: Mentor

    Completing the square is a good way to begin. Afterwards, a clever substitution can help.
  4. Mar 14, 2013 #3
    okay. im stuck with the subtracted term.

    [itex]\frac{1}{-\sqrt{(x^2 - 8x + 16) - 16}}[/itex]

    [itex]\frac{1}{-\sqrt{(x-4)^2 - 16}}[/itex]
  5. Mar 14, 2013 #4
    i don't think completing the square works here.
  6. Mar 14, 2013 #5


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    Homework Helper

    Looks like you pulled a negative outside of the square root. You can't do that!!!! Try again.
  7. Mar 14, 2013 #6
    Once you've fixed up the negative, try the substitution u=(x-4) and then consider what the derivatives of the inverse trigonometric functions look like.
  8. Mar 14, 2013 #7
    great. thanks phosgene.

    so we are looking at:

    [itex]arcsin(\frac{x-4}{4}) + c[/itex]
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