Yeah, in this case it's a bit misplaced. The first thing your high school calculus course would have you do would be called “u-substitution”, and if you did dir

Yeah, in this case it's a bit misplaced. The first thing your high school calculus course would have you do would be called “u-substitution”, and if you did directly u = x √(a), du = √(a) dx you would get the same immediately, or if you did something stranger like u = a x², dx = ½ du/√(a u) you would get (1/√a) ∫ exp(-u) u^-½ du which furnishes a handy proof that (-½)! = √π, once you know the Gaussian integral.