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Q: How to find this integral $\int_{0}^{1}\ln\ln\bigl(1/x+\sqrt{(1/x^2)-1}\,\bigr)dx$

china math How do I compute this integral ? $$I=\int_{0}^{1}\ln{\left(\ln{\left(\dfrac{1}{x}+\sqrt{\dfrac{1}{x^2}-1}\right)}\right)}dx$$ In the math chatroom someone suggests setting $x=\operatorname{sech}(t)$ and that the result immediately follows. I don't agree with it because $$\dfrac{1}{x...

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