I have to integrate the following and I was having trouble with it because I am pretty new to the concept of using partial fractions. I did as much as I could and I need help in moving forward:
$$\int\frac{x^5+3x^2+1}{x^5+x^2}dx$$
I did some long division and got:
$$\int1+\frac{2x^2+1}{x^5+x^2}dx$$
Factored the denominator:
$$x^5+x^2$$
and got the following:
$$x^2(x+1)(x^2-x+1)$$
Now I think that I should have something like this, but I'm not sure:
$$\frac{A}{x^2}+\frac{B}{x+1}+\frac{C}{x^2-x+1}$$
Would appreciate any help. Thanks.