Question

Evaluate the Integral:

Answer 1

Wherre is it ?

Answer 2

\[\int\limits_{}^{}\frac{ 2x^4-4x^3+13x^2-6x+10 }{ (x-2)(x^2-2x+5) }dx\]

Answer 3

I just need help with the partial fraction decomposition.

Answer 4

Huh?

Answer 5

@goformit100

Answer 6

Anyone?

Answer 7

i am doing hw for pfd also so i may be able to work on this with you

Answer 8

TI-89

Answer 9

TI-89 cant be used in my class lol.
let me try and figure this out @diddo525 i think that since this is a high degree in the neumirator we will have to do division first

Answer 10

No it's not. Expand the bottom. The denominator is greater than the numerator for the degree.

Answer 11

well its only \[x^3-4x^2+9x-10\]

Answer 12

yeah

Answer 13

Never mind. I got it. It's really really ugly though >.< .

Answer 14

man i hate to say it but im stumped, we just started learning it, could you explain?

Answer 15

Thanks anyways :) .

Answer 16

Allright. The denominator has an irreducible quadratic right?

Answer 17

Because we can't factor it in any way.

Answer 18

yeah

Answer 19

So forget about that for now. We can rewrite the fraction as:

\[\frac{ A }{x-2 } + \frac{ Bx+c }{ x^2-2x+5 }+\frac{ Dx+E }{ (x^2-2x+5)^2 }\]

Answer 20

Whenever we have an irreducible quadratic, we can rewrite the numerator with a linear function like I did.

Answer 21

Does that make sense?

Answer 22

@sjerman1

Answer 23

sorry
yes, yes it does

Answer 24

\[(-20A-10B+9C-2D+E)x+(14A+9B-4c+D)x^2+(-4A-4B+c)x^3+(A+B)x^4+25A-10C-2E\]

Answer 25

We set each term equal to the corresponding degree in the original polynomial: