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!