Trên khoảng \(\left( {0; + \infty } \right)\), cho hàm số \(f\left( x \right) = {x^{\frac{3}{2}}}\). Mệnh đề nào sau đây đúng?

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

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

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

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

A. \[x\sqrt[5]{x} - 2x\sqrt[{17}]{{{x^5}}} + \sqrt[4]{{{x^3}}} + C\].

B. \[\frac{4}{5}x\sqrt[5]{x} - \frac{{24}}{{17}}x\sqrt[{17}]{{{x^5}}} + \frac{4}{3}\sqrt[4]{{{x^3}}} + C\].

C. \[x\sqrt[5]{x} - \frac{{24}}{{17}}x\sqrt[{17}]{{{x^5}}} + \sqrt[4]{{{x^3}}} + C\].

D. \[\frac{4}{5}x\sqrt[5]{x} - 2x\sqrt[{17}]{{{x^5}}} + \frac{4}{3}\sqrt[4]{{{x^3}}} + C\].

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

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

A. \(f\left( x \right) = 6{x^2} - 2\)

B. \(f\left( x \right) = \frac{1}{2}{x^4} - {x^2} + x\)

C. \(f\left( x \right) = \frac{1}{2}{x^4} - {x^2} + x + C\).

D. \(f\left( x \right) = 6{x^2} - 2 + C\).