## mony01 2 years ago anybody know how to do this integral?

1. mony01

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

2. myininaya

you can try partial fractions

3. mony01

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

4. myininaya

Can I see what you have so far?

5. mony01

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

6. myininaya

You can find C pretty fast by letting x be 2

7. myininaya

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

8. myininaya

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

9. mony01

is C=-5 and A=10

10. myininaya

yep

11. mony01

B=-9 when x=1

12. myininaya

yep

13. mony01

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

14. myininaya

You mean integrate it?

15. myininaya

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

16. mony01

yea

17. hartnn

where are you stuck now?