Solving Confusing Integral Equations

[acedeno]

Homework Statement

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

Homework Equations

Integral chart

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!

 

[Dickfore]

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

 

[acedeno]

Not following.

 

[Dickfore]

Your dummy variable is x, your upper limit contains x.

 

[SammyS]

Not following.

Is this the integral?

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

 

[acedeno]

Is this the integral?

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

Yes, that is the integral.

 

[SammyS]

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 .

 

[Dickfore]

No, use the substitution:

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

 

[flyingpig]

No, use the substitution:

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

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