# Confusing Integral!

1. Sep 29, 2011

### acedeno

1. The problem statement, all variables and given/known data

int[x/((L/2)+d-x)^2] * the integral of x over [(L over 2 + d - x) all squared]*

2. Relevant equations
Integral chart

3. The attempt at a solution
I have done this so many ways with so many different answers. Could somebody who is without a doubt sure of the answer please respond because this integral is driving me INSANE!

2. Sep 29, 2011

### Dickfore

You can't have x in the upper limit and as an integration dummy variable.

3. Sep 29, 2011

### acedeno

Not following.

4. Sep 29, 2011

### Dickfore

5. Sep 29, 2011

### SammyS

Staff Emeritus
Is this the integral?

$\displaystyle \int\frac{x}{((L/2)+d-x)^2}\ dx$

6. Sep 29, 2011

### acedeno

Yes, that is the integral.

7. Sep 29, 2011

### SammyS

Staff Emeritus
To simplify things, Let A = (L/2) + d .

Your integral becomes: $\displaystyle \int\frac{x}{(A-x)^2}\ dx$

Notice the (A - x)2 = (x - A)2.

Use the substitution: u = x - A .

8. Sep 30, 2011

### Dickfore

No, use the substitution:

$$u = (x - A)^{2}$$

9. Sep 30, 2011

### flyingpig

No unique substitution, but Sammy's substation is easier to work with