I want to evaluate $$\int_{a+b-c}^s\,\text{d}x\, \frac{(-x+ab/c)^{\epsilon}}{(x+c-a-b)^{\epsilon+1} (a-x)},$$ where $a,b,c,\epsilon$ are real numbers, and to be treated as constants in the integration. I put this into mathematica and an hour later it is still attempting to evaluate it so I aborted the calculation. I was just wondering if it is possible to make headway on the calculation analytically?
I tried partial fractions which gave a rewriting of the form $$\frac{1}{c-b}\int_{a+b-c}^{s} \text{d}x\, \frac{(-x+ab/c)^{\epsilon}}{(x+c-a-b)^{\epsilon}} \left(\frac{1}{x+c-a-b} + \frac{1}{a-x}\right)$$ $$ = \frac{1}{c-b}\left(\int_{a+b-c}^{s} \text{d}x\, \frac{(-x+ab/c)^{\epsilon}}{(x+c-a-b)^{\epsilon+1}} + \int_{a+b-c}^{s} \text{d}x\, \frac{(-x+ab/c)^{\epsilon}}{(x+c-a-b)^{\epsilon}} \frac{1}{a-x}\right)$$ but this probably did not help.
Thanks!