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How To Integrate This?

  1. Jun 16, 2013 #1
    How to integrate below?

    $$\int \sqrt{\frac{r^{2}-x^{2}+x^{2}}{r^{2}-x^{2}}} dx$$

    neither if u = r^2 - x^2 nor u = x^2 will get the result.
  2. jcsd
  3. Jun 16, 2013 #2


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    Staff: Mentor

    Try u=x/r, and simplify, it should become a standard integral (solvable with formulas, or with a trigonometric substitution)
  4. Jun 16, 2013 #3


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    Is this really what you meant? Since [itex]-x^2+ x^2= 0[/itex] the is exactly the same as
    [tex]|r|\int \frac{1}{\sqrt{r^2- x^2}}dx[/tex]

    The substitution x= sin(t) would be a stadard technique for this.
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