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Calculus with inverse trig functions

  1. Sep 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Evaluate the integral of (1/Sqrt(5x-x^2))


    2. Relevant equations
    [d/dx]{arcsin(x)}=(du/dx)/sqrt(1-x^2)


    3. The attempt at a solution
    arcsine(2x-5)/5


    I did end up getting the right answer, but have no idea how I got there.
     
  2. jcsd
  3. Sep 2, 2009 #2

    rock.freak667

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    So we have

    [tex]\int \frac{1}{\sqrt{5x-x^2}}[/tex]

    try completing the square for 5x-x2 (i.e. put it into the form a[x+h]2+k)
     
  4. Sep 2, 2009 #3
    I have tried that, but the 5 is what is throwing me off.
     
  5. Sep 2, 2009 #4

    rock.freak667

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    5x-x2 = -(x2-5x) = -(x+5/2)2+k. Can you find 'k'?
     
  6. Sep 2, 2009 #5
    thank you very much
     
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