Here is the problem: $\int \frac{5x^2-2}{x^2-4x-12}dx$
I factored it and got this form:
$\int \frac{5x^2-2}{(x-6)(x+2)}dx$ however the solution shows the next step looking like this: $\int 5+ \frac{20x+58}{(x-6)(x+2)}dx$
I know how to integrate and solve it, but this particular step has me confused. Can you help me to explain how they got there?
The reason I'm confused is because the following steps show the actual decomposition using A, B, etc over their respective denominators.
Edit: Now that I look at it, it looks like they divided it, but I don't understand why there is still a decomposition if the problem can be divided.