This is just an alternative notation for making a substitution in an integral. If you replace by in the right-hand integral then it becomes , which exactly what you would get by making the substitution in the left-hand integral.
Umm, I'm not quite sure how to ask this....
How do you do that? What's going on here? As in changing dx to d(x^2). Is this a method I haven't been taught?....or do I not fully understand the concept of "with respect to x"? I see that d(x^2) equals 2x giving you the same integral but I need further clarification....
Thanks.