integrate ((3x-1)/(x^2-x-1))

Question

anonymous · Answer

$$\int\limits_{}^{}\frac{ 3x-1 }{ x^2-x-1}$$

amistre64 · Answer

what is the derivative of the bottom?

anonymous · Answer

2x-1

amistre64 · Answer

hmmm, then my first idea wont work

amistre64 · Answer

might have to go ahead and partialdecomp it

amistre64 · Answer

what is the factorization of the denom?

anonymous · Answer

(x-1/2)^2 -3/4

amistre64 · Answer

..... you are not gonna like what the wolf brought up

anonymous · Answer

i been there couldn't make head or tail of it

amistre64 · Answer

http://www.wolframalpha.com/input/?i=integrate+%283x-1%29%2F%28x%5E2-x-1%29 this tells me that its goona best be down by decomposition

amistre64 · Answer

x^2-x-1
(x-1/4)^2 -5/4
x = 1/4 + sqrt(5)/4
x = 1/4 -  sqrt(5)/4

(x -1/4 -sqrt(5)/4) (x -1/4 + sqrt(5)/4)  oy that hurts

$$3x-1 =A(x -\frac14 -\frac{\sqrt{5}}4)+B(x -\frac14 + \frac{\sqrt{5}}4)$$

amistre64 · Answer

when x=1/4 + sqrt(5)/4

$$3(\frac14 + \frac{\sqrt{5}}4)-1 =A(0)+B(\frac{2\sqrt{5}}4)$$
$$\frac{2(\frac34 + \frac{3\sqrt{5}}4-1)}{\sqrt5} =B$$

amistre64 · Answer

same concept for finding A, then it logs up just fine; but oy what a mess

amistre64 · Answer

did i do the factoring right?

anonymous · Answer

isn't it (x-1/2)^2-5/4

amistre64 · Answer

yeah, i got 4s underneath and they need to be 2s :/

amistre64 · Answer

same mes tho :)

anonymous · Answer

yeah, thx a million

amistre64 · Answer

good luck ;)