Partial Fractions Integration

I generally understand partial fractions, but this problem is a little more complex. I've tried it a few different ways, and I'm still stuck.

I need to integrate (7x^2 + 2x - 4) / (x^3 + 2x^2)

Thank you so much for reading, and I would really, really appreciate it if anyone could help me out!

(7x^2 + 2x - 4) / (x^3 + 2x^2)
= (7x²+2x-4)/[x²(x+2)]
= A/x² + B/x + C/(x+2)

7x²+2x-4 = Ax+2A+Bx²+2Bx+Cx²
2A = -4 ==> A = -2
A+2B = 2 ==> B = 2
B+C = 7 ==> C = 5

f(x) = (7x²+2x-4)/(x³+2x²) = -2/x² +2/x + 5/(x+2)
int(f(x)dx) = -2*int(dx/x²) + 2*int(dx/x) + 5*int[dx/(x+2)]

= 2/x + 2lnx + 5ln(x+2) + C

A / x + B / x^2 + C / (x + 2) = (7x^2 + 2x - 4) / (x^3 + 2x^2)

A * x * (x + 2) + B * (x + 2) + C * x^2 = 7x^2 + 2x - 4
A * (x^2 + 2x) + B * (x + 2) + Cx^2 = 7x^2 + 2x - 4
Ax^2 + 2Ax + Bx + 2B + Cx^2 = 7x^2 + 2x - 4

Ax^2 + Cx^2 = 7x^2
2Ax + Bx = 2x
2B = -4

B = -2

2A + B = 2
2A - 2 = 2
2A = 4
A = 2

A + C = 7
2 + C = 7
C = 5

2 / x - 2 / x^2 + 5 / (x + 2)