Bài tập Nguyên hàm của hàm số lũy thừa lớp 12 (có lời giải)

A. 2x + C;

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

C. x³ + C;

D. 3x³ + C.

A. 6x + C;

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

C. x³ + C;

D. x³ + x + C.

A. 3x² + 1 + C;

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

C. x³ + x + C;

D. x⁴ + x² + C.

A. F(x) = x⁵ – 2x⁴ – 3x² + C;

B. F(x) = x⁵ – x⁴ – x² + C;

C. F(x) = x⁵ – 4x⁴ – 2x² + C;

D. F(x) = x⁵ + 2x⁴ – 3x² + C.

A. \(F\left( x \right) = \frac{1}{3}{x^3} + \frac{3}{2}{x^2} + 2x + C\);

B. \(F\left( x \right) = \frac{1}{3}{x^3} + \frac{2}{3}{x^2} + 2x + C\);

C. F(x) = 2x + 3 + C;

D. \(F\left( x \right) = \frac{1}{3}{x^3} - \frac{2}{3}{x^2} + 2x + C\).

A. \({f_1}\left( x \right) = \frac{1}{{3\sqrt[3]{{{x^2}}}}} + \frac{1}{{\sqrt x }} + \frac{3}{2}\sqrt x \);

B. \({f_2}\left( x \right) = \frac{1}{{3\sqrt[3]{{{x^2}}}}} + \frac{1}{{\sqrt x }} + \frac{3}{{2\sqrt x }}\);

C. \({f_3}\left( x \right) = \frac{{\sqrt[3]{{{x^2}}}}}{3} + \frac{1}{{\sqrt x }} + \frac{3}{2}\sqrt x \);

D. \({f_4}\left( x \right) = \frac{1}{{3\sqrt[3]{{{x^2}}}}} + \frac{1}{2}\sqrt x + \frac{3}{{2\sqrt x }}\).

A. −ln|x + 2| + C;

B. ln|x + 2| + C;

C. (x + 2) + C;

D. \(\frac{1}{{{{\left( {x + 2} \right)}^2}}} + C\).

A. \( - \frac{1}{3}\ln \left| {3x + 1} \right| + C\);

B. \(\frac{1}{3}\ln \left| {3x + 1} \right| + C\);

C. \(\frac{1}{3}\ln \left| {3x - 1} \right| + C\);

D. \( - \frac{1}{3}{\left( {3x + 1} \right)^{\frac{2}{3}}} + C\).

A. \(\frac{{{x^3}}}{3} - \frac{3}{2}{x^2} + \ln \left| x \right| + C\);

B. \(\frac{{{x^3}}}{2} - \frac{2}{3}{x^2} + \ln \left| x \right| + C\);

C. \(\frac{{{x^3}}}{2} - \frac{C}{3}{x^2} + \ln \left| x \right|\);

D. \(\frac{{{x^3}}}{3} - \frac{C}{3}{x^2} + \ln \left| x \right|\).

A. \(\frac{{2{x^3}}}{3} - \frac{3}{x} + C\);

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

C. \(2{x^3} + \frac{3}{x} + C\);

D. \(2{x^3} + \frac{3}{{{x^2}}} + C\).