i need to find the definite integral from 0 to 2|b| of ....

x divided by sqrt(x^2 + b^2) dx

im having a lot of trouble, thanks in advance

Let u = x^2 + b^2
du = 2x dx
The integrand becomes
(1/2) u^(-1/2) du
and the integral of this is u^(1/2)
= sqrt(x^2 + b^2)
Evaluate this between your limits.

First set u = x^2 + b^2
du = 2(x+b)or 2x + 2b

It would be very tedious to try to solve this on line with no signs for integral, radical, etc. But above is the first step to solving this problem. You must first find du. As you can see, you'll have some messy exponents to work with, something that would be very difficult to do here.

Is b a constant? This entire thing is crazy. Where is the dx?

If b is a constant,

du=2x dx