And in case it isn't clear, I should point out that there is no simple formula for finding the antiderivative of any general rational function. Some such functions will not even have elementary antiderivatives. It all depends on exactly what the fraction consists of.
This is characteristic of integration in general. With differentiation, you can find the derivative of any elementary function (if it exists) by using the sheer mechanical application of some straightforward rules. With integration, this is not so.
For the antiderivative of your specific expression, follow Jhevon's suggestion and use partial fraction decomposition.