# 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!

## Answers and Replies

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

Not following.

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

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