Impossible Integration involving cosx/sqrt(a-bcosx)

[flux!]

Ok, I have encountered this one a few hours ago:
$$\int \frac{cos x}{\sqrt{a - b cos x}}dx$$
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?

 

[Dr. Courtney]

Wolfram Alpha? Integral table?

 

[mfig]

Mathematica returns the same result found in Gradshteyn and Ryzhik.

 

[Dr. Courtney]

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.

 

[flux!]

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.