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You would probably use a power-reduction trig identity to solve this equation.
This states that sin2(x) = (1 - cos(2x))/2
Therefore, sin2(2x) = (1 - cos(4x))/2, or (1/2)(1 - cos(4x))
So, ∫ (1/2)(1 - cos(4x)) dx = (1/2) ∫ (1 - cos(4x)) dx.
Then, ∫ (1-cos4x)dx = x - (1/4)sin(4x) + c
Now, multiply that by (1/2) to get:
(x - (sin(4x)/4) + c)/2
Since c is an arbitrary constant, we have:
½(x - sin(4x) / 4) + c
OR
1/8 * (4x - sin(4x)) + c
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