Question

Integrate 3x+6/x^2-3x+2

so i just need help with the end of the problem....

i have x(A+B)+A(-1)+B(-2)=3x+6

@pgpilot326

Answer 1

i got A=9 and B=-9

Answer 2

gotta do it the hard way, huh?

Answer 3

don't you get
\[\frac{3x+6}{x^{2}-3x+2}=\frac{A}{x-1}+\frac{B}{x-2}\]

Answer 4

i have to write it out on my homework:/

Answer 5

then do what @satellite73 was showing you ...

Answer 6

my -1 and -2 are switched on mine bt yeah

Answer 7

so from yours...

A+B=3 and
-A-2B=6

just solve the system

Answer 8

\[\frac{3x+6}{(x-2)(x-1)}=\frac{A}{x-2}+\frac{B}{x-1}\]
\[A=\frac{3\times 2+6}{2-1}\]

Answer 9

\(B=-9\) is correct, yes

Answer 10

9ln(abs(x-2))-9ln(abs(x-1))+c so why isnt my answer right?:(

Answer 11

because \(A=12\) not \(9\)

Answer 12

12 ln(abs(x-2)) -8ln(abs(x-1)) +C

Answer 13

oops... 9 not 8

Answer 14

let me check my math

Answer 15

\[A=\frac{3\times 2+6}{2-1}=\frac{12}{1}=12\]

Answer 16

got it! thank you!!!

Answer 17

\[\frac{ 3x+6 }{x ^{2}-3x+2 }=\frac{ 3x+6 }{x ^{2}-2x-1x+2 }=\frac{3x+6 }{ x \left( x-2 \right)-1(x-2) }\]
\[=\frac{ 3x+6 }{ \left( x-2 \right)\left( x-1 \right) }=\frac{3*2+6 }{\left( x-2 \right)\left( 2-1 \right) }+\frac{ 3*1+6 }{\left( 1-2 \right)(x-1) }\]
\[=\frac{ 12 }{ x-2 }-\frac{ 9 }{x-1 }\]
now you can integrate.