Question

Partial fraction decomposition: 1/(x³ - 8x² + 17x)

Answer 1

\[\frac{8-x}{17 \left(x^2-8 x+17\right)}+\frac{1}{17 x} \]

Answer 2

How did you get that?

Answer 3

Refer to:
http://jwbales.us/precal/part7/part7.6.html

I used Mathematica 8 Home Edition. Selected your expression with the mouse and then clicked on the "Apart" button found on the Algebraic Manipulation palette. Instant answer.

Answer 4

I understand the idea but do you know how x^3-8x^2+17x can be factored o.o? Does Mathematica show this?

Answer 5

\[\frac{1}{x \left(x^2-8 x+17\right)}=\frac{8-x}{17 \left(x^2-8 x+17\right)}+\frac{1}{17 x} \]

Answer 6

There is a "Factor" button on the same palette referenced above and is used in the same manner as the "Apart" button. I used the Factor button first and then did the Apart in that order for the equation above. If Mathematica cannot factor a polynomial, then it probably is not factorable.

Answer 7

Hmm interesting... Cause my main question in fact was to integrate what I just asked, and figured I could attempt it with partial fractions

Answer 8

\[\int\limits \left(\frac{8-x}{17 \left(x^2-8 x+17\right)}+\frac{1}{17 x}\right) \, dx= \]\[-\frac{4}{17} \text{ArcTan}[4-x]+\frac{\text{Log}[x]}{17}-\frac{1}{34} \text{Log}\left[17-8 x+x^2\right]+C \]

Answer 9

well i suppose with software it's easy o.O But doing it by hand? Oye o_O??

Answer 10

I cannot integrate x^2 with pencil and paper if my life depended on it. That is why Mathematica was written.

www.WolframAlpha.com will do your integrations for you. They are the folks who wrote and are continually improving the Mathematica program.

Answer 11

lol ok. Well you know I think i have a better idea on how to do it tho, the answer sorta hints at what I could possibly do

Answer 12

So thanks :P

Answer 13

Your welcome.