Question

find the partial fraction decomposition

Answer 1

\[\int\limits_{?}^{?} \frac{ 5x^2+2x+1 }{ (x-1)(x+1)^2 }\]

Answer 2

the answer is 2/x-1+3/x+1-2/(x+1)^2

Answer 3

i dont know how it got that cause i got 8/3 for A 4/3 for B and 5 for C

Answer 4

i have A/x-1 B/x+1 and C/(x+1)^2

Answer 5

ok, break the integrand to \(\dfrac{A}{x-1}+\dfrac{B}{x+1}+\dfrac{C}{(x+1)^2}\)

Answer 6

next?

Answer 7

yep did that i do wrong is the canceling out part

Answer 8

show me your work so that I might find out your mistake

Answer 9

:)

Answer 10

okay after that i did

Answer 11

yup, now just pick the numerator to calculate

Answer 12

A(x+1)^2 + B(x-1)(x+1) + C(x-1)= 5x^2 +2x+1

Answer 13

don't go on that way. hehehe, try my way

Answer 14

if x = -1, then the first term (involve A) and the second term (involve B) =0, right?

Answer 15

the left hand side remains C(-1-1) = -2C

Answer 16

the right hand side (5*(-1)^2 +2(-1) +1)= 4
hence -2C=4 , C =-2

Answer 17

so far so good???

Answer 18

yeah

Answer 19

Now, if x =1, your turn, hehehe, just imitate mine

Answer 20

this is better than the other method where you cancel out the As and Bs and Cs

Answer 21

For this method, you can assign x =0, -1, .... whatever you like to find A, B, C

Answer 22

you said use 0 for the second one right

Answer 23

use 1

Answer 24

why not 0

Answer 25

why 1? because if x =1, (x-1) =0 that make the second term and the third one "disappear"

Answer 26

you have just A

Answer 27

oh okay i see

Answer 28

I mean something involve A

Answer 29

i got 2=A

Answer 30

:( I got A =4

Answer 31

lol i think thats wrong cause the answer is 2/x-1+3/x+1-2/(x+1)^2

Answer 32

oh, you are right, hehehe.. since A(x+1)^2 , hence the left hand side is A(1+1)^2 = 4A and the right hand side is 8 , hence A =2
my stupid brain!!

Answer 33

Go ahead , my friend!! woo woo!!

Answer 34

lol you are not stupid i am the stupid one without you i could have never done this problem

Answer 35

I think you can handle the leftover now, right?

Answer 36

yeah thank you so much

Answer 37

ok