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Evaluating an indefinite integral

  1. Aug 13, 2011 #1
    1. The problem statement, all variables and given/known data

    Evaluate the integral

    [itex]\int \frac{(a-x)^{r/s-1}}{(b-x)^{r/2}}dx[/itex]

    2. Relevant equations

    given: s>r

    3. The attempt at a solution

    I tried using a substitution:
    let u=b-x
    so du=-dx
    this gives:

    [itex]-\int \frac{(a-b+u)^{r/s-1}}{u^{r/2}}du[/itex]

    I don't know what i should do after this, and i think this substitution will take me nowhere.

    Does anyone have any ideas?

    Thank you in advance
    .
     
  2. jcsd
  3. Aug 13, 2011 #2

    SammyS

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    Is the exponent in the numerator (r/s)-1, or is it r/(s-1) ?
     
  4. Aug 14, 2011 #3
    the exponent is (r/s)-1
     
  5. Aug 14, 2011 #4

    I like Serena

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    Hi sara_87! :smile:

    I believe there is no solution for your integral using only a finite number of standard functions.

    If you feed it to WolframAlpha:
    http://www.wolframalpha.com/input/?i=\int+\frac{%28a-x%29^{r%2Fs-1}}{%28b-x%29^{r%2F2}}dx
    WolframAlpha comes up with a Hypergeometric function F.
    With this F your integral can be expressed, but as far as I'm concerned that's just another way of saying it does not have a regular solution.

    To use your integral in practice, you'd normally use a numerical approximation.
     
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