Tính \(\int {\frac{{\sqrt x - 2\sqrt[3]{{{x^2}}} + 1}}{{\sqrt[4]{x}}}dx} \).

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. \(\frac{4}{{15}}x\sqrt[{15}]{{{x^7}}} + C\).

B. \(\frac{8}{{15}}x\sqrt[{15}]{{{x^7}}} + C\).

C. \(\frac{8}{{15}}x\sqrt[{15}]{x} + C\).

D. \(\frac{4}{{15}}x\sqrt[{15}]{x} + C\).

A. \(\int {f\left( x \right)} dx = \frac{3}{2}{x^{\frac{1}{2}}} + C\).

B. \(\int {f\left( x \right)} dx = \int {\sqrt {{x^3}} } dx\).

C. \(\int {f\left( x \right)} dx = \frac{2}{5}{x^{\frac{5}{2}}} + C\).

D. \(\int {f\left( x \right)} dx = \frac{2}{3}{x^{\frac{1}{2}}} + C\).

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

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

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

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

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

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

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

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

A. \(\int {\left( {2\sin x + 3x} \right)dx = - 2\cos x + \frac{3}{2}{x^2} + C} \)

B. \(\int {\left( {2\sin x + 3x} \right)dx = 2\cos x + 3{x^2} + C} \)

C. \(\int {\left( {2\sin x + 3x} \right)dx = {{\sin }^2}x + \frac{3}{2}x + C} \)

D. \(\int {\left( {2\sin x + 3x} \right)dx = \sin 2x + \frac{3}{2}{x^2} + C} \)