
Consider the following integrals
$\int_0^{2 \pi} \ln(\sin(x)^{2n+1} + C_n) = 0$
All of the $C_n$ are algebraic numbers.
In fact all these $C_n$ can be given as zero's of some integer polynomial with degree $v$ where $0<v<2n+2$.
Conjecture 1 : All these $C_n$ are algebraic numbers of degree exactl...