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2. Write tan^2(2x) as sec^2(2x)-1 [Using identity tan^2(x)+1=sec^2(x)

3. Let sec2x=t

Differentiating both sides we get, 2sec(2x)tan(2x)dx = dt

4. Multiply and divide integral by 2

it becomes 1/2*integration ( tan^3(u)sec(u)du )

=1/2*(integration ( tan(u)sec(u)(sec^2(u) - 1) )

substitute s=sec(u) and ds=tan(u)sec(u)

so you get 1/2*(integration ( (s^2 - 1) ds)

=s^3/6 - s/2 + c

=1/6*sec^3(2x) - 1/2*sec(2x) + c.