Integration of Rational Functions by Partial Fractions
Hey guys i'm a bit confused and clueless when it comes to writing out the form of the partial fraction decomposition of the function.
Maybe you guys can help me understand through examples.
2 / (x^2 + 3x - 4)
now I know I can factor the Q(x) to (x + 4)(x - 1)
So the partial fractioning for this will be (A / (x + 4)) + (B / (x - 1)) right? I have no problems doing simple ones such as this.
Now here is an example of one of which i'm totally clueless as where the extra factors are coming from.
1 / (x^6 - x^3)
now I can factor the Q(x) to (x^3)(x - 1)(x^2 +x + 1). Now how would I partial fraction this and the most important WHY? The "WHY" is what I really need most. Thanks