Nguyên hàm của hàm số \[f(x) = \] \(\frac{1}{3}{x^3} - 2{x^2} + x - 2024\) là

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

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

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

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

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

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

B. \(\frac{{{x^2}}}{2} - \cos x + C\).

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

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

A. \(f\left( x \right) = - \sin x\).

B. \(f\left( x \right) = - \cos x\).

C. \(f\left( x \right) = \sin x\).

D. \(f\left( x \right) = \cos x\).

A. \[\int {f(x)dx = } F(x) + C\].

B. \({\left( {\int {f(x)dx} } \right)^\prime } = f(x)\).

C. \({\left( {\int {f(x)dx} } \right)^\prime } = f'(x)\).

D. \({\left( {\int {f(x)dx} } \right)^\prime } = F'(x)\).

A. \(2x + C\).

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

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

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