What is the integral of sqrt(4cos^2(2x)+4sin^2(2x)) ?

The integral of sqrt(4cos^2(2x)+4sin^2(2x)) is 2x+C

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integral of sqrt(4cos^2(2x)+4sin^2(2x))

\int 4 cos^{2} (2 x) + 4 sin^{2} (2 x) d x

2 x + C

Solution steps

\int 4 cos^{2} (2 x) + 4 sin^{2} (2 x) d x

4 cos^{2} (2 x) + 4 sin^{2} (2 x) = 2

= \int 2 d x

Integral of a constant:

\int a d x = a x

= 2 x

Add a constant to the solution

= 2 x + C

What is the integral of sqrt(4cos^2(2x)+4sin^2(2x)) ?
The integral of sqrt(4cos^2(2x)+4sin^2(2x)) is 2x+C