Find the Integral sec(2x)^2

Let . Then , so . Rewrite using and .
Let . Find .
Rewrite.
Divide by .
Rewrite the problem using and .
Combine and .
Since is constant with respect to , move out of the integral.
Since the derivative of is , the integral of is .
Simplify.
Replace all occurrences of with .
Find the Integral sec(2x)^2