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Prove one of the following...

DreamWeaver

Well-known member
Sep 16, 2013
337
There's a unified pattern at work here...



Problem 1:

[tex]\int_0^{\infty}\frac{\log(1-\sin x)}{x}\,dx=-\frac{\pi^2}{6}=-\zeta(2)[/tex]



Problem 2:

[tex]\int_0^{\infty}\frac{ \text{Li}_m(\sin x) }{x}\,dx=\text{Li}_{m+1}(1)=\zeta (m+1)[/tex]