Evaluating an indefinite integral

[sara_87]

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.

 

[SammyS]

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

 

[sara_87]

the exponent is (r/s)-1

 

[I like Serena]

Hi sara_87!

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.