Integral solve only using

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How can I solve $$\int \sqrt{1+\cos(6x)} \,dx$$ only using algebraic, trigonometric methods, immediate integrals and integral properties?

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HINT:

Use $$\cos2y=2\cos^2y-1$$

and $$\int\cos mxdx=\frac{\sin mx}m+C$$ for $m\ne0$ and $C$ is an arbitrary constant