Taking the square of a formula

[Pual Black]

Homework Statement

Hi sorry if the titel is wrong

I want to know if i can write this

$a^2 + u^2 -2au= (a-u)^2 = (u-a)^2$
I get different results when integrating $x^{-\frac{3}{2}}$ in the range $(a-u)^2$ to $(a+u)^2$

 

[Mark44]

Homework Statement

Hi sorry if the titel is wrong

I want to know if i can write this

$a^2 + u^2 -2au= (a-u)^2 = (u-a)^2$

Yes, these expressions are all equal.

I get different results when integrating $x^{-\frac{3}{2}}$ in the range $(a-u)^2$ to $(a+u)^2$

It would be helpful to see your work.

 

[Pual Black]

I've uploaded my work as images.
Sorry for not using LaTex but I am on mobile phone.

 

[Mark44]

I've uploaded my work as images.
Sorry for not using LaTex but I am on mobile phone.

I think the problem might be from taking the square root of (a - u)². It's not necessarily equal to a - u. What is true is that $\sqrt{(a - u)^2} = |a - u|$ which in turn is equal to $|u - a|$.

 

[Pual Black]

Ok i got it.
Thank you for your help