The discussion revolves around the evaluation of the integral $$\int_{0}^{1}t\cos(2t\pi)\tan(t\pi)\ln[\sin(t\pi)]\mathrm dt$$ and whether it can be shown to equal $$\color{green}{1\over \pi}\cdot\color{blue}{{\ln 2\over 2}(1-\ln 2)}.$$ The scope includes mathematical reasoning and potentially exploratory approaches to solving the integral.
Participants generally agree on the need for hints to solve the integral, but no consensus on a method or solution exists as the discussion remains unresolved.
The discussion lacks specific mathematical techniques or assumptions that could lead to a resolution, and the participants have not provided any steps or approaches to evaluate the integral.
Readers interested in integral calculus, particularly those looking for collaborative problem-solving approaches in advanced mathematics.
can I get the hint?lfdahl said:A hint is requested ... (Blush)