Question

anybody know how to do this integral?

Answer 1

\[\int\limits \frac{ x ^{2} +1}{ (x-3)(x-2)^{2} }dx\]

Answer 2

you can try partial fractions

Answer 3

im stuck in the part where you have to find A,B, and C

Answer 4

Can I see what you have so far?

Answer 5

x^2+1=A(x-2)^2+B(x-2)(x-3)+C(x-3)

Answer 6

You can find C pretty fast by letting x be 2

Answer 7

You can find A pretty fast also by letting x be 3

Answer 8

You have two unknown values which it leaves you with the one, B.
You can replace A with whatever you found and replace C with whatever you found and then use any value for x besides 2 or 3 to find B

Answer 9

is C=-5 and A=10

Answer 10

yep

Answer 11

B=-9 when x=1

Answer 12

yep

Answer 13

when putting it all together how can i simplify -5/(x-2)^2?

Answer 14

You mean integrate it?

Answer 15

how would you integrate -5/u^2 with respect to u?

Answer 16

yea

Answer 17

where are you stuck now?