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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- Nov 20th 2009, 07:43 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.

- Nov 20th 2009, 07:50 AMlvleph
You can use the third factor:

C will a function of x. - Nov 20th 2009, 08:23 AMTWiX
- Nov 20th 2009, 08:45 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))? - Nov 20th 2009, 01:04 PMTWiX
- Nov 20th 2009, 09:01 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

- Nov 21st 2009, 03:53 AMshadow85
umm wasnt the second post, enough to solve this?

- Nov 21st 2009, 08:58 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.