Umm, I'm not quite sure how to ask this....

$\displaystyle

\int {x^3 e^{x^2 } } dx = \tfrac{1}

{2}\int {x^2 e^{x^2 } } d(x^2 )

$

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.