I saw this method of calculating:(adsbygoogle = window.adsbygoogle || []).push({});

$$I = \int_{0}^{1} \log^2(1-x)\log^2(x) dx$$

http://math.stackexchange.com/questions/959701/evaluate-int1-0-log21-x-log2x-dx

Can you take a look at M.N.C.E.'s method?

I dont understand a few things.

Somehow he makes the relation:

$$\frac{4H_n}{(n+1)(n+2)^3} = \frac{\left( \gamma + \psi(-z) \right)^2}{(z+1)(z+2)^3}$$

How is this established?

And this I dont understand,why did he integrate it,?

And then after he states: "At the positive integers,"what is he doing with the residues. I know the residue theorem etc, but I dont understand what he is exactly doing?

Thanks

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# Explain this method for integrals (complex analysis)

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