Question

Need help integrating x^3/(x-2)^2.

Answer 1

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.

Answer 2

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)

Answer 3

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

Answer 4

Please help.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

when integrated you get the above

Answer 12

Ok. Thanks!