Question

Integrate

9/x(x^(2)+9)

I have tried both ways to do this and I'm consistently getting the incorrect answer

Roots = 0, 3, -3

(A/x) + (Bx + C)/(x^(2) + 9)x

(A(x^(2) +9) + x(Bx + C))/(x^(2) + 9)x

0| 1 = A
3| 0 = 9B + 3C - 9
-3 | 0 = 9B + -3C - 9
I don't remember where to go from here

I tried this method and I still got the wrong answer.
(A/x) + B/(x-3) + C/(x+3)
(A(x-3)(x+3) + B(x+3)x + C(x-3)x)/x(x-3)(x+3)

0 | 9 = -A9, A = -1
3 | 9 = B18, B = 1/2
-3 | 9 = C18, C = 1/2

These solutions are in correct can someone show me where I'm going wrong with applyin

Answer 1

applying this method, for both cases

Answer 2

if its x^2 +9, then the roots are wrong

x^2 -9 = (x+3)(x-3)
x^2 +9 has no real roots

Answer 3

so I have to use the first method

Answer 4

you can still use partial fractions though
\[= \frac{A}{x} + \frac{Bx+C}{x^{2}+9}\]
=(A+B)x^2 +Cx +9A
--> A+B =0
C = 0
A = 1

Answer 5

did I at least perform the 2nd method correctly (even though I got the wrong answer)?

Answer 6

you can use the first method if you don't mind using 3i and -3i

Answer 7

Haven't learned about imaginary numbers :\ so I tend to avoid them

Answer 8

An integrations solution is attached.

Answer 9

This question is more about applying this method then it is finding the answer

Answer 10

Is the correct answer 9lnx -9/2*ln(x^2+9)?

Answer 11

The answer is ln|x| - (1/2)ln|x^(2) + 9| + C

Answer 12

yes it looks like you applied it correctly on 2nd method

Answer 13

How do I use the first method? to find B and C

Answer 14

Big booboo by me on the PF part, 9a=9 --> a=1.

Answer 15

I believe the faulth in your PF is the ending x here: (A/x) + (Bx + C)/(x^(2) + 9)>>x<<

Answer 16

You should get (A/x) + (Bx + C)/(x^(2) + 9) ---> A(X^2+9)+BX^2+CX
Leading to 9A=9 and A+B=0 --> B=-A=-1
I'm not sure this helps, sorry.

Answer 17

so I should expand it to

(A(x^(2) + 9)+ Bx^(2) + Cx)/x(x^(2)+9)

9 = Bx^(2) + Cx
Im lost at this part still :l I can't recall how to solve this

Answer 18

look back at my post
group the x^2 terms and the x terms and the constants
the constants will equal 9, the rest set equal to 0

Answer 19

(A(x^(2) + 9)+ Bx^(2) + Cx)/x(x^(2)+9) is correct.
Moreover, you know that you only need a 9 meaning A+B has to be zero. Because of x^2(A+B)
The only variable you have not "influenced" by an x is A so 9A=9 --> A=1

Answer 20

Listen to smartcow.

Answer 21

:)

Answer 22

:)