Question

Why for this int (3x^2-x+1)/(x^3-2x^2) we use (A/x)+(B/x^2)+(C/x-2) And for this int (3x^2-x+1)/(x^3-x^2) we use (A/x^2)+(B/x-1) Why the first int we considered case I (fraction partial) and the second one we use case II? Sorry for my english

Answer 1

The first case (partial fraction) is the right one for both expressions.
In second case, simly, I guess a short way to solve the problem.

Explanation:

The right partial fraction decomposition:

`(3x^2-x+1)/(x^3-x^2)=(Ax+B)/x^2+C/(x-1)= A/x+B/(x^2)+C/(x-1)`