How to obtain the explicit formula of the following integral $$\int\limits_0^1 {{t^{ - 1 - x}}\left( {{{\left( {1 + t} \right)}^{ - y}} - 1} \right)} dt,\;x,y \in \left( { - 1,1} \right).$$ It can be expressed in terms of hypergeometric function？
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On first look it seems to me like one could probably transofrm the above in a Beta-type integral https://en.wikipedia.org/wiki/Beta_function – May 23 '17 at 13:34
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2$$\int_0^1t^{-1-x}\left((1+t)^{-y}-1\right)\ dt=B(-x,1-y)-\int_0^1t^{-1-x}\ dt=B(-x,1-y)+\frac1x$$ – Simply Beautiful Art May 23 '17 at 13:55