# Homework Help: How to integrate x^2/(1-x)

1. Jun 25, 2010

### sallaboy

1. The problem statement, all variables and given/known data
x^2/(1-x)

2. Relevant equations
none

3. The attempt at a solution
I know I should use some kind of substitute but ... may t=1-x but what next ?

any help will be helpfull
thanks dimitry

2. Jun 25, 2010

### Phrak

using t=1-x replace x in your integrand with x = 1-t. Also dx is replaced.

Find dt as a function of dx.

3. Jun 25, 2010

### sallaboy

ok ... but can I use the same technic when I have:

x^2/(x+2)

?

4. Jun 25, 2010

### rl.bhat

You can rewrite the problem as

(x^2 - 4 + 4)/(x+2)

= (x^2 - 4 )/(x+2) + 4/(x+2)

Now simplify and find the integration.

5. Jun 25, 2010

### sallaboy

thanks a lot !!!

6. Jun 25, 2010

### gomunkul51

if the degree of the polynomial in the nominator is equal or higher the the degree of the polynomial in the denominator the you have to do polynomial long division to turn the expression to a whole part plus a rational quotient (a fraction with a polynomial in the nominator of a lesser degree then the polynomial in the denominator).

7. Jun 25, 2010

### njama

Another idea:

u=1-x

du=dx

x=1-u

8. Jun 25, 2010

### Staff: Mentor

IMO, this is the simplest approach of those presented here.
x^2/(1 - x) = -x^2/(x -1) = -x - 1 - 1/(x - 1).

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook