The value of \(\int {\cos }^{2}xdxis-\)

\(\frac{x}{2}+\frac{1}{4}\sin 2x+\mathrm{C}\)

\({x}^{2}+\frac{1}{4}\sin 2x+C\)

\(\frac{x}{4}+\frac{1}{2}\sin x+C\)

\(\frac{{x}^{2}}{2}+\frac{1}{2}{\sin }^{2}x+C\)