# Homework Help: Answer to \ 2/(x-2)^3 dx

1. Jan 14, 2007

### lost_math

1. The problem statement, all variables and given/known data
\ 2/(x-2)^3 dx
Basically integrating a perfect cube in the denominator with a constant in the numerator

2. Relevant equations

3. The attempt at a solution
i thought it would be a form of ln(x), but then, that would mean having atleast some x terms in the numerator which are not there, so, how do i do this? Is there a known pre-fixed solution for these things? Like exp(something)?

2. Jan 14, 2007

### arunbg

Use $$\int x^ndx = \frac{x^{n+1}}{n+1} + c$$

Last edited: Jan 15, 2007
3. Jan 14, 2007

### cristo

Staff Emeritus
Try writing as 2(x-2)-3. Do you know how to integrate x-3?

4. Jan 14, 2007

### lost_math

Thanks Arun and Cristo.
Cristo, I dont know how to integrate x^-3. (i think i might be hopeless, right?)
Arun, what is the expansion formula you just gave me called? Is there a name for solving by that method? It is applicable to negative powers as well?

5. Jan 14, 2007

### cristo

Staff Emeritus
Arunbg's formula is the formula for integrating a polynomial function of x. Thus, to integrate x-3 you would use that formula.

6. Jan 14, 2007

### sara_87

you want to integrate 2(x-2)-3

using this $$\int x^n = \frac{x^{n+1}}{n+1} + c$$

the first thing you notice is that you add 1 to the power, then you divided by the new power
after that you multiply by the differntial of what is inside the brackets

7. Jan 14, 2007

### sara_87

in your question the power is -3

8. Jan 14, 2007

### cristo

Staff Emeritus
The last bit should read: you divide by the derivative of the term inside the brackets.

(I know it's probably a typo, and it doesn't matter in this case; but it may confuse the OP in future if left uncorrected)

9. Jan 14, 2007

### sara_87

yes definitely a typo
you always divid by the differential of the inside of the brackets when integrating!