Interesting integration problem

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Homework Help Overview

The discussion revolves around an indefinite integral involving constants A and B, specifically the expression ∫{[A+(1/x²-Bx)]^1/2}dx. Participants are exploring methods to approach this integration problem.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to solve the integral by expanding the root and using a crude approximation. Other participants question whether the integral is definite or indefinite and suggest considering numerical methods for evaluation.

Discussion Status

The conversation is ongoing, with some participants providing suggestions for numerical integration methods, while others express skepticism about the existence of a simple anti-derivative for the given integral. There is no clear consensus on the best approach yet.

Contextual Notes

The problem is identified as a homework task, and the original poster is seeking a numerical solution despite the integral being indefinite. There is a mention of looking for an algorithm for numerical integration.

collpitt
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Homework Statement


In the given integral, both A and B are constants.


Homework Equations



∫{[A+(1/x²-Bx)]^1/2}dx


The Attempt at a Solution


Well, I have solved the problem by expanding the root and considering the first two terms only,
but it gives a very crude approximation of the required result.
Anyone having any ideas or comments, please do reply.

Thank you.
 
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Is this a problem in a homework or something? I can't see how to do it. Was it a definite or indefinite integral? If definite, can you do something numerical?
 
Well actually it is sort of a homework problem and unfortunately, it is indefinite. I am looking for a numerical solution by defining the limits. It would be very helpful if you could give me a good algorithm for the numerical integration.

Thank you!
 
Well, for an algorithm, just google Simpson's Rule. (Try the 3/8 one first).

But, I don't really see how this will help if the integral is indefinite. What you really need is an anti-derivative and I just don't think that a non-really-complicated one exists.
 

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