## anonymous 4 years ago Need help integrating x^3/(x-2)^2.

1. anonymous

I started with long division and got x + 4 as the quotient and 12x - 16 as th remainder. I'm not sure if thats correct.

2. anonymous

Then I wrote it as the sum of the integral of each term. So like, (int) x + (int) 4 + (int)(12/(x-2)^2) - (int) (16/(x-2 )^2)

3. anonymous

I'm not sure if I'm doing this right so far. :(

4. anonymous

5. lalaly

thats right, but its supposed to be 8/(x-2)^2 not 16

6. lalaly

and one more thing, 12/(x-2)

7. anonymous

I'm not sure how you got those. Are they a result of long division?

8. anonymous

they are the result of long division, lalaly is right.

9. anonymous

so you have (int) x + (int) 12/(x-2) + (int) 8/(x+2)^2 + (int) 4

10. anonymous

$x^2/2+12\ln(x-2)-8/(x-2)+4x+C$

11. anonymous

when integrated you get the above

12. anonymous

Ok. Thanks!