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CAF123
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Homework Statement
Integrate $$\int_0^1 dw \frac{w^{\epsilon+1} \ln((r+1-w)/r)}{1+r(1+w)}$$ for ##\epsilon## not necessarily an integer but positive and r is negative (<-1). The argument of the log is positive.
Homework Equations
Integration by parts
The Attempt at a Solution
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I can only think of integration by parts, differentiating the log to bring back the rational but I wouldn't be able to integrate the remaining piece of the integrand. I suspect the result will be a hypergeometric function but I can't seem to get there. I had a similar integral with ##\ln (w)## instead and my prof suggested I write this as $$\ln w = \frac{d}{d\beta} w^{\beta}|_{\beta=0} = \frac{d}{d\beta} e^{\beta \ln w}|_{\beta=0}$$ but I am not sure why this helps.
Thanks for any help!