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in this video were going to talk about how to integrate rational functions using partial fraction decomposition so the first thing we want to do is make sure that this integral is completely factored on the bottom we have a difference of perfect squares and so we can factor that expression by taking the square root of x squared which is x and the square root of four which is two one is going to be positive two the other will be negative two so what we have on the bottom is two distinct linear factors now you might be wondering what is the difference between a linear factor and a quadratic factor linear factors include examples such as x 3x x plus 4 4x minus 5 those are linear factors quadratic factors they typically have an x squared so x squared x squared plus 4 thats a quadratic factor x squared plus 3x thats another one or x squared plus 2x plus 7. those are quadratic factors now to use the technique of partial fraction decomposition what were going to do is were going to brea
