Can the Integral of x*sin(x)^-1 be Solved using the Li Function?

[KingNothing]

How does one solve this integral?
<br /> \int {x * \left( {\sin x} \right)} ^{ - 1} dx<br />

 

[Zelos]

http://integrals.wolfram.com/index.jsp"
using that

 

[arildno]

By numerical means, i would presume.

 

[KingNothing]

I would appreciate some sincere responses on how to solve it, by hand.

 

[HallsofIvy]

You were given two "sincere" responses. The "anti-derivative" of that is not an "elementary" function. According to the web-site Zelos gave you that involves the "Li" function.