2
The following integral was proposed in a paper by O. Furdui, namely
$$\int_0^1 \log^2(\sqrt{1+x}-\sqrt{1-x}) \ dx$$
and then the generalization
$$\int_0^1 \log^2(\sqrt[k]{1+x}-\sqrt[k]{1-x}) \ dx$$
As regards the first integral, my approach was to combine the integration by parts and the va...