Tedious or elegant ?

Level pending

Let \(C_r(\alpha) = \displaystyle \frac{\alpha(\alpha-1)(\alpha-2)...(\alpha-r+1)}{r!}\). Then evaluate the definite integral

\(\displaystyle \int_{0}^{1} C_{2015}(-y-1)\left(\frac{1}{y+1}+\frac{1}{y+2}+...+\frac{1}{y+2015}\right) dy\)

*This is a modified problem....

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