I need some help to evaluate the following integral.
∫∞0dxxα(x+1) where α∈(0,1)
I've tried many ways (the best one seems to be developing by Taylor series) but actually I have no solution.
Some ideas?
Thank you.
Answer
I think we will need some complex analysis here.
Take a branch of 1/za defined in C∖[0,+∞) and consider the integral
∫γdzza(z+1)
where γ is a close path composed by an arc of a inner circle of radius $0
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