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

  • Thread starter KingNothing
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In summary, the limits of integration for an integral are typically provided in the problem statement. If not, they can be determined by identifying the points where the function intersects the x-axis. Substitution is a common technique for solving integrals, which involves replacing a variable with a new one to simplify the problem. The best method for solving a trigonometric integral depends on the specific problem, such as using trigonometric identities, integration by parts, or substitution. Integrals are generally solvable if the function is continuous on the interval of integration, but may require advanced techniques or numerical methods. Calculators and computer programs can be used to solve integrals, but it is important to have an understanding of the concepts and techniques involved.
  • #1
KingNothing
882
4
How does one solve this integral?
[tex]
\int {x * \left( {\sin x} \right)} ^{ - 1} dx
[/tex]
 
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  • #2
http://integrals.wolfram.com/index.jsp"
using that
 
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  • #3
By numerical means, i would presume.
 
  • #4
I would appreciate some sincere responses on how to solve it, by hand.
 
  • #5
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.
 

1. How do I determine the limits of integration for an integral?

The limits of integration for an integral are typically given in the problem statement. If they are not explicitly stated, you can determine them by looking at the function being integrated and identifying the points where it intersects the x-axis.

2. Can I use substitution to solve this integral?

Yes, substitution is a common technique used to solve integrals. It involves replacing a variable in the integral with a new variable in order to simplify the problem.

3. What is the best method for solving a trigonometric integral?

The best method for solving a trigonometric integral depends on the specific problem. Some common techniques include using trigonometric identities, integration by parts, and substitution.

4. How do I know if an integral is solvable?

In general, integrals are solvable as long as the function being integrated is continuous on the interval of integration. However, some integrals may require advanced techniques or numerical methods to solve.

5. Can I use a calculator to solve an integral?

Yes, there are many calculators and computer programs available that can solve integrals. However, it is important to understand the concepts and techniques behind solving integrals in order to use these tools effectively.

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