- Thread starter
- #1

#### DreamWeaver

##### Well-known member

- Sep 16, 2013

- 337

**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]