# Thread: integral of a+bcosx form

1. ## integral of a+bcosx form

This is my first post to this forum, so I wish to start by saying hello to all of you who take time out of your schedule to help those of us with questions. As a teacher, I know how valuable this is! My question involves finding out the technique for solving the following integral:

$\int {\frac{{\cos xdx}}{{{{\left( {a - b\cos x} \right)}^2}}}}$

According to a German table of integrals, I have found the following clue:

$\int {\frac{{\cos xdx}}{{{{\left( {a + b\cos x} \right)}^2}}}} = \frac{1}{{{a^2} - {b^2}}}\left( {\frac{{a\sin x}}{{a + b\cos x}} - b\int {\frac{{dx}}{{a + b\cos x}}} } \right)$

I have tried a number of different approaches, but I have not found a step by step solution to the integral. Any suggestions would be appreciated!

2. ## Re: integral of a+bcosx form

Do you have any reason to believe that can be integrated in closed form?

3. ## Re: integral of a+bcosx form

I probably should have worked on the problem for a couple more days before posting, because I was able to solve the integral at last. I ended up using a partial fraction decomposition to split it into two integrals, then used a recurrence formula technique to solve the first of the two integrals, and finally a Weierstrass substitution to solve the second integral.