# Integration partial fractions

1. Jan 1, 2009

### noobie!

1. The problem statement, all variables and given/known data
integrate (4x^2 + 3x + 6)/x^2 (x+2) dx

2. Relevant equations
don't have sorry..

3. The attempt at a solution
firstly = A/x + B/x^2 + C /x+2 , = A(x^2)(x+2) + B(x)(x+2) + C(x)(x^2) equating with the 4x^2 + 3x + 6,then i integrate it,but my ans turn out to be wrong..so could you please rectify my mistakes..thanks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 1, 2009

### tiny-tim

happy new year!

Hi noobie!!
Nooo … too many x's!

get some sleep :zzz:

then try again!

3. Jan 1, 2009

### FedEx

Try to obtain the numerator as a derivative of the denominator. And then the extra term which you get try to break it in simple parts.

4. Jan 1, 2009

### Unco

Hi Noobie,

If you have

$$\frac{4x^2+3x+6}{x^2(x+2)} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x+2}$$

then multiplying through gives

$$4x^2 + 3x + 6 = Ax(x+2) + B(x+2) + Cx^2$$.

Now you can equate coefficients as you intended to.

5. Jan 2, 2009

### FedEx

Unco the method which you did is the same which noobie has presented. It contains too many x's. There is an another nice way of doing it.

6. Jan 3, 2009

### noobie!

ok,i understand..thanks a lot..

7. Jan 3, 2009

### FedEx

Understood! What did you do with the remaining term?