# Confusing Integral!

## Homework Statement

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

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!

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

Not following.

SammyS
Staff Emeritus
Homework Helper
Gold Member
Not following.
Is this the integral?

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

Is this the integral?

$\displaystyle \int\frac{x}{((L/2)+d-x)^2}\ dx$
Yes, that is the integral.

SammyS
Staff Emeritus
Homework Helper
Gold Member
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 .

No, use the substitution:

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

No, use the substitution:

$$u = (x - A)^{2}$$
No unique substitution, but Sammy's substation is easier to work with