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Calculus with inverse trig functions

  • Thread starter famallama
  • Start date
  • #1
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Homework Statement


Evaluate the integral of (1/Sqrt(5x-x^2))


Homework Equations


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


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.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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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)
 
  • #3
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I have tried that, but the 5 is what is throwing me off.
 
  • #4
rock.freak667
Homework Helper
6,230
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I have tried that, but the 5 is what is throwing me off.
5x-x2 = -(x2-5x) = -(x+5/2)2+k. Can you find 'k'?
 
  • #5
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thank you very much
 

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