Anti derivative of ( (x-1) / (x-d) ) ^ 0.5 * x ^ c

[NumaNuma]

Hey all,

I'm working on a problem and it boils down to finding the anti-derivative of the following expression:

((x-1)/(x-a))^0.5 * x^b

I have tried loads of substitutions, but nothing has worked so far. I'm not really sure if the anti-derivative exists, but I'd really want to find it if it does.

Any help will be greatly appreciated.

Thanks

 

[ksdhart2]

For certain, specific values of a or b, the integral would be trivial, like if a = 1 or b = 0. However, the general form is much more difficult. WolframAlpha says that the indefinite integral of the expression you posted involves the Appell Hypergeometric Function. So, I don't think it's possible to integrate using only elementary operations, unless you can discern the values of a and b (which you might be able to do, if there was other information in the problem which you haven't posted). If you'd be willing to share with us the full and exact text of the problem, quoting word-for-word if possible, that would help a lot. Thank you.