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

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Discussion Overview

The discussion centers around the integral of the function \( x \cdot \left( \sin x \right)^{-1} \), exploring methods for solving it, including the potential use of the Li function. The scope includes both analytical and numerical approaches to integration.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant inquires about methods to solve the integral by hand.
  • Another participant suggests that numerical methods may be appropriate for this integral.
  • A third participant asserts that the integral does not have an elementary antiderivative and references the Li function as a potential solution.
  • There is a request for more detailed and sincere responses regarding the hand-solution of the integral.

Areas of Agreement / Disagreement

Participants express differing views on the solvability of the integral, with some suggesting numerical methods while others reference the Li function, indicating a lack of consensus on a straightforward analytical solution.

Contextual Notes

There is an implication that the integral's solution may depend on definitions and the nature of the functions involved, particularly regarding the classification of the antiderivative.

KingNothing
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How does one solve this integral?
[tex] \int {x * \left( {\sin x} \right)} ^{ - 1} dx[/tex]
 
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http://integrals.wolfram.com/index.jsp"
using that
 
Last edited by a moderator:
By numerical means, i would presume.
 
I would appreciate some sincere responses on how to solve it, by hand.
 
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.
 

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