I need help solving:

integral of (20x-30) / (x(x-2)(x^2-2x+5))

If I try to decompose it;

I will have

LHS from above = (A/x)+(B/x-2) + ?

Stuck here.

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- November 20th 2009, 06:43 AMshadow85Partial fraction question
I need help solving:

integral of (20x-30) / (x(x-2)(x^2-2x+5))

If I try to decompose it;

I will have

LHS from above = (A/x)+(B/x-2) + ?

Stuck here.

- November 20th 2009, 06:50 AMlvleph
You can use the third factor:

C will a function of x. - November 20th 2009, 07:23 AMTWiX
- November 20th 2009, 07:45 AMshadow85
ohh I see, but I didnt think the polynomial could be there under Cx+D because its not factored?

So, now I am suppose to multiply both sides by (x(x-2)(x^2-2x+5))? - November 20th 2009, 12:04 PMTWiX
- November 20th 2009, 08:01 PMsimplependulum

If we let

and we know

The original fraction can be expressed in the form of :

we can see the last term

the numerator is a polynomial with degree , that means

we do not need to break it down into pieces anymore .

If we continue , we can obtain

- November 21st 2009, 02:53 AMshadow85
umm wasnt the second post, enough to solve this?

- November 21st 2009, 07:58 AMlvleph
Not quite, because you to solve you would have to have a polynomial in the third fraction. I did say that C was a polynomial, but I didn't say of what order.