Interesting integration problem

[collpitt]

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.

 

[Robert1986]

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?

 

[collpitt]

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!

 

[Robert1986]

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.