\[\int {{{\left( {\sin \frac{x}{2} + \cos \frac{x}{2}} \right)}^2}{\rm{d}}x} \] bằng:

B. A. \(F\left( x \right) = 2\cos \frac{x}{2} + C\)

C. B. \(F\left( x \right) = \frac{1}{2}\left( {1 + \sin x} \right) + C\)

D. C. \(F\left( x \right) = 2\sin \frac{x}{2} + C\)

A. D. \(F\left( x \right) = \frac{1}{2}\left( {1 - \sin x} \right) + C\)

A. \[{x^2} + C\].

B. \[{x^2} + 6x + C\].

C. \[2{x^2} + C\].

D. \[2{x^2} + 6x + C\].

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

B. \(3{x^2} + 1 + C\)

C. \({x^3} + x + C\)

D. \({x^4} + {x^2} + C\)

A. \[\frac{1}{5}{x^5} + \frac{1}{3}{x^3} + C\]

B. \[{x^4} + {x^2} + C\]

C. \[{x^5} + {x^3} + C\].

D. \[4{x^3} + 2x + C\]

A. \(\frac{{{x^{2023}}}}{{2023}} + 1\).

B. \(\frac{{{x^{2023}}}}{{2023}}\).

C. \(y = 2022{x^{2021}}\).

D. \(\frac{{{x^{2023}}}}{{2023}} - 1\).

A. \[\frac{1}{{12}}{x^4} - \frac{2}{3}{x^3} + \frac{{{x^2}}}{2} + C\].

B. \(\frac{1}{9}{x^4} - \frac{2}{3}{x^3} + \frac{{{x^2}}}{2} - 2024x + C\).

C. \(\frac{1}{{12}}{x^4} - \frac{2}{3}{x^3} + \frac{{{x^2}}}{2} - 2024x + C\).

D. \(\frac{1}{9}{x^4} + \frac{2}{3}{x^3} - \frac{{{x^2}}}{2} - 2024x + C\).

A. \[F\left( x \right)\, = \,\frac{{{x^4}}}{4}\, - \,6{x^3}\, + \,\frac{{11}}{2}{x^2} - \,6x\, + \,C\].B. \[F\left( x \right)\, = \,{x^4}\, + \,6{x^3}\, + \,11{x^2} + \,6x\, + \,C\].

C. \[F\left( x \right)\, = \,\frac{{{x^4}}}{4}\, + 2{x^3}\, + \,\frac{{11}}{2}{x^2} + \,6x\, + \,C\].D. \[F\left( x \right)\, = \,{x^3}\, + \,6{x^2}\, + \,11{x^2} + \,6x\, + \,C\].