# Thread: integration (x^2-x+6)/(x^3+3x) dx by parts

1. ## integration (x^2-x+6)/(x^3+3x) dx by parts

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

I get stuck when im trying to find what a b and c should be.

2. I don't know what a, b or c are and it looks like you've tried to include an image; could you edit the post please so that I can help?

3. ## Re: integration (x^2-x+6)/(x^3+3x) dx by parts

Originally Posted by summergrl
integrate (x^2-x+6)/(x^3+3x) dx

I get stuck when im trying to find what a b and c should be.
What "a", "b", and "c"? There is only "x" in your integrand.

Please reply with clarification, including a clear listing of all of your work and reasoning so far.

Thank you.

Eliz.

4. sorry...the image was there by mistake.
I am pretty sure I need to use integration by parts and we use A, B, and C.
So so far i seperated it into
A/X + (Bx+C)/(x^2+3)

5. I think you mean partial fractions, not integration by parts.

$\L \frac{x^2 - x + 6}{x(x^2 + 3)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 3}$

$\L \frac{x^2 - x + 6}{x(x^2 + 3)} = \frac{A(x^2+3)}{x(x^2+3)} + \frac{x(Bx + C)}{x(x^2 + 3)}$

$\L x^2 - x + 6 = A(x^2 + 3) + x(Bx + C)$

$\L x^2 - x + 6 = (A + B)x^2 + Cx + 3A$

equate coefficients ...

$\L A + B = 1$
$\L C = -1$
$\L 3A = 6$

can you finish?

6. oops! i keep on mixing those two names up.
how do you know A+b=1?

7. $\L x^2 - x + 6 = (A+B)x^2 + Cx + 3A$

look at the left side of the equation ... what is the coefficient of x<sup>2</sup>?

look at the right side of the equation ... what is the coefficient of x<sup>2</sup>?

now set the coeffcients equal.

8. If you know about complex numbers you can do it much faster...

9. Originally Posted by Count Iblis
If you know about complex numbers you can do it much faster...
... and if only pigs could fly.

10. okay thanks! i understand that part now...so I got B=-1, C=-1, and A =2.
then i get the integration of
(2/x) - (x/x^2+3) - (1/x^2+3)
and i get 2lnx - 1/2ln(x^2+3) but then i don't know how to do the third part. Does it have anything to do with arctan?

p.s. whats this talk about pigs?? hehe

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