How Do You Solve Integration Using Partial Fractions?

[noobie!]

Homework Statement

integrate (4x^2 + 3x + 6)/x^2 (x+2) dx

Homework Equations

don't have sorry..

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

 

[tiny-tim]

happy new year!

Hi noobie!

(4x^2 + 3x + 6)/x^2 (x+2) dx
…
= 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

Nooo … too many x's!

get some sleep :zzz:

then try again! ​

 

[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.

 

[Unco]

Hi Noobie,

Homework Statement

integrate (4x^2 + 3x + 6)/(x^2 (x+2)) dx

Homework Equations

don't have sorry..

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

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.

 

[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.

 

[noobie!]

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.

ok,i understand..thanks a lot..

 

[FedEx]

ok,i understand..thanks a lot..

Understood! What did you do with the remaining term?