Evaluating an indefinite integral

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Homework Help Overview

The discussion revolves around evaluating the indefinite integral of the form \(\int \frac{(a-x)^{r/s-1}}{(b-x)^{r/2}}dx\), with the condition that \(s > r\). Participants are exploring the complexities involved in finding a solution.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts a substitution method but expresses uncertainty about its effectiveness. A participant questions the exponent in the numerator, leading to clarification on its form. Another participant suggests that the integral may not have a solution in terms of standard functions and mentions the use of numerical approximations.

Discussion Status

The discussion is active, with participants clarifying details about the integral and exploring the possibility of expressing it in terms of special functions. There is no consensus on a straightforward solution, but some guidance regarding numerical methods has been introduced.

Contextual Notes

Participants are working under the assumption that the integral cannot be solved using a finite number of standard functions, which is a significant constraint in their exploration.

sara_87
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Homework Statement



Evaluate the integral

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

Homework Equations



given: s>r

The Attempt at a Solution



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

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

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.
 
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Is the exponent in the numerator (r/s)-1, or is it r/(s-1) ?
 
the exponent is (r/s)-1
 
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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