How to integrate this function?

In summary, the conversation is about studying Landau Mechanics in chapter III, specifically §15 Kepler's problem on page 36. The variables M, m, E, and α are constant in this problem. The question is how to integrate it and the suggestion is to use integral tables and reference books like Schaums outlines on Math Tables and Formulas. The person who asked for help has solved the problem and wants to know how to delete the article, but is informed that questions with useful responses are not deleted on the forum.
  • #1
physicophysiology
12
3
Hello
I am studying Landau Mechanics (3rd ed.)

In chapter III Integration of the Equations of Motions
§15. Kepler's problem
page 36
Howtointegrateit.png

M(angular momentum), m(mass), E(mechanical energy), and α are constant.

How to integrate it?
Please help me...
 

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  • #2
If you’re just trying to verify that’s it’s true then differentiate the integrated side to prove to yourself.

To integrate it though, I would use integral tables and look up a similar one. There is no shame in using this approach as there are many integrals that vex even the best folks.

A cheap book with integral tables is Schaums outlines on Math Tables and Formulas. It’s available on Amazon and is a great reference to keep around.
 
  • #3
physicophysiologist said:
I SOLVED IT
HOW CAN I DELETE THIS ARTICLE?
Welcome to the PF. We do not delete questions that have useful responses.
 
  • #4
You could share your solution here as this thread will get indexed on Google and other search engines benefitting others studying Landau.
 
Last edited:
  • #5
berkeman said:
Welcome to the PF. We do not delete questions that have useful responses.
Original post restored in post #1.
 

1. What is integration?

Integration is a mathematical process that involves finding the area under a curve on a graph. It is the reverse operation of differentiation, which involves finding the slope of a curve at a specific point.

2. Why do we need to integrate functions?

Integrating functions allows us to find the total or accumulated value of a function over a given interval. This can be useful in many applications, such as calculating displacement, velocity, and acceleration in physics, or finding the total cost or revenue in economics.

3. How do you find the integral of a function?

To find the integral of a function, we must use integration techniques such as substitution, integration by parts, or trigonometric substitution. These techniques involve manipulating the function algebraically to find the antiderivative, or the original function before it was differentiated.

4. What are some common mistakes to avoid when integrating functions?

Some common mistakes when integrating functions include forgetting to add the constant of integration, not using the proper integration technique for a given function, and making errors in algebraic manipulations. It is important to check your work and double-check the final answer to avoid these mistakes.

5. How can I practice and improve my integration skills?

The best way to improve your integration skills is to practice solving a variety of integration problems. You can find practice problems in textbooks, online resources, or by creating your own integrals. Additionally, seeking help from a tutor, professor, or online resources can also aid in improving your skills.

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