Impossible Integration involving cosx/sqrt(a-bcosx)

In summary, the conversation revolves around the difficulty of integrating the given expression and the use of different techniques and resources to solve it. The conversation also mentions the convenience of using tools such as Wolfram Alpha and integration tables, but acknowledges the limitations of relying on them during exams.
  • #1
flux!
34
0
Ok, I have encountered this one a few hours ago:
[tex]\int \frac{cos x}{\sqrt{a - b cos x}}dx [/tex]
I have tried all techniques I know, integration by part, half-angle formula, substitution, trigo approach, and so on, but it seems, I could not integrate this one. I am no noob in integration, but this one is a bit difficult. How do I integrate it?
 
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  • #3
Mathematica returns the same result found in Gradshteyn and Ryzhik.
 
  • #4
I suspected that. After I learned that a lot of integrals cannot be solved without essentially defining a new function (like erf and the ellipticals), I got in the habit after spinning my wheels a bit with the standard techniques of looking them up in G&R to see if they were do-able.

When MMa came along, it was faster than looking in G&R. WA is even more convenient.
 
  • #5
Yes of course, it is really convenient to look into table of integrals, but it is just impossible to do on exams. I hope we could have a technique to solve it.
 

1. What is "Impossible Integration involving cosx/sqrt(a-bcosx)"?

"Impossible Integration involving cosx/sqrt(a-bcosx)" refers to a type of integration problem in calculus that involves the trigonometric function cosine (cosx) and a square root expression with a variable (a) and the cosine function (bcosx).

2. Why is it called "impossible integration"?

This type of integration problem is often referred to as "impossible" because there is no known analytical method to solve it. It requires the use of advanced mathematical techniques and approximations to find a solution.

3. Can this type of integration problem be solved?

Yes, it can be solved using numerical methods such as numerical integration or by approximating the integral using a Taylor series expansion.

4. What are the common applications of "Impossible Integration involving cosx/sqrt(a-bcosx)"?

This type of integration problem often arises in physics and engineering, specifically in problems involving oscillatory motion, such as pendulums or springs.

5. Are there any tips for solving "Impossible Integration involving cosx/sqrt(a-bcosx)"?

One tip for solving this type of integration problem is to use trigonometric identities and substitution to simplify the expression before attempting to integrate. It may also be helpful to break the integral into smaller parts and use numerical methods to approximate the solution.

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