Evaluate the definite Integral

Question

Integral [0 to pi/4] cos(2x)sec^2(pi/4 sin(2x))dx

Answer 1

Let u = tan(π/4 sin(2x))
du = sec^2(π/4 sin(2x))*(π/4)(2cos(2x)) du

So, what you have is just ∫du with some constant factored out.